Elementa geometriae

Page 130

I ; ' r-----.,~ LIGER b cumigifllT\'fNq) cmmnnlincaru;.a.b.'l.R.d.fit oiuifa fm,ppo11ionC :~:;,~~.;medium ouoq3 eytrctna:isif cncpcr ptcmiffli ~mb;;qz ipfllJZ a_d fut mal toteS po!lionm ,·1111 ,ppottio. itatp.d .. a. ad.a .b.quc dl o~J smaiot po:no f1cur.a: b db quccfl cti.i cmgrnato:pomofcd:d.a.ad.a.b.f!Cut.a.b .Gd.b.d.c;co•f.• ni~o~f·l~;ICC oiuifc Mn plopottionou babdtrcm mcd!un• 011oq; CJ.trclllil 'ln~alot ponto cine :igiwr c;c vndcchlutqutnu.a .b.ad.b.d. f1cut.a .b.od. b.c .quar.._ PI:~ fccundJ r.rcm .9 .qulnti.b.d. 'Z.b.c .funt cqmdco.cum cril;~-~-d. ftt iJtL~IJ occ?so•n crit quoq~ c.t ,6i fdo.b.C-13ruo oaagoni.ll~l ~litcr11d hnCJ:a·?-lldttiiiJ)Ilt .b._d: c.qu~ba ,b.c.crltt}3 ey •4•1Tcd~Orr~i 1~!\l.\l,d, 0.\Uifll (,11 ,~0}(~01\C bll\>ct.I(C_ mc_dl~l) oooq) q.mm'l t maiot po:110 cL91mca:o.b:uoq.l pcrcouafa.9.m:dccmu ~na 'o ~ rin~c poll ipf.i ocm61lmuimu\J cuiua cmuh hncu .. b.dlbtu~ qgg~nl ~u\dc;_ll "ca.b.d.idcoq; \inca.b.c.ftbi cqualt<l (larue occasoni •. J)~l~un~t~o trc;: \(k; o.ha \'Ia fi hlxt ocmon\lrorc.Sit cni .c.f._cqml~i\3.\l.b._quc~t~\l 01mdo.r t.g. ~m ;PP~:tt~ nfi»>X ri rncdul 01toq) c~rron11 oz fu ma.to:. pomo C\ \mca! .. s.~llar !B't c~ pnuf f ll cp quf:adntoi):o. .b.( c~li\l.C. f. ftC.Il.C .C cqlia.c. 6· -;_.c.b9 cqho.g: f.c_uq; fuqft .b d.sdiiim ad.l1.b.IJt9 ooagoni tilt" e~rcuh cm'.ll .b:' Ill c~gont c;tt ftQtt pnus oicrU ic~ . 9 .ncdccimi toro..ll.d.oinifa ~~~~ ..PpOl~io!t' babcmc mcdut ouoq; CJtrc m~r t maiooci'ponio a:'t linCil.ll.b.ir~cp v.pnu~a.11:~ lld.b.d.ftrut.f.g:.lld 5·'.: qrc P. j)lmi part(. 15 Jc~tt~O fi! c~.11.b.m . g.c.cquu ~ '! q~od ftt ~"J.b.~.m.f.g .ctt IU·a.b.fit cqualill.d . ..: cn~qO ft! C1.c.f.m.l).c.cquu c .~ qtl ftt C.J:.b :d.m.f.g .Sed quod fit q:.c.f. in .g.c.cquu ell quadraro. f.g .c1 01ffm1tt:>ttc bn~c. t!_t~nf~ f.m ,ppol/ rionC babcnwn mcdiulll Ottoq; c~tro:ma ozq pJIUHt [tc.tdo;n:_tstr qo fu cy.b.d. in.f.g.cll cqna!c quaduuo.f.g.tdcoq; q: p:itna fc1nltnca .b. d_.c _cqualh;.f.g:.t q: f.g.( cqllil.i\'l,C.b.crit quoq;.c.b.cqual:o:.b.d. 'l tuuu o«agont qo opo:tcb\tt otlc dcrc. · 1ibzopofitio ·•· &a.dratU latcrio pctttllgoni intra. dr1.11Ium Oc.'"cripri qn:~; ramm quclillccquc illiuo pcmagoui angu!o fiJbtcnd1t omiJo t>CC<lu•.•Jrora po~i·rc~,"cccpra qu11dran medicmno ~~~~:~~:::r~t~:~~~~~c~~~~!'~ic~::!:~~~~.~~~~~~p~~~~~~~~::~~~~~liiO couilalcrua ~iuo ..-nii la1us ftr.a.b.oz: p:otrabaf Oiamctcr .c.d.c. Oiuidmolincam a.'b.'lchl!."!Mrcti percqualia. fili6(lur arcu\'l.a.c.mcdtcfll9quintcQtiocircfifcrcn tic illiuo drculi quarcarcus.a.c.C oucquimc totitll3 circiifcr(ntic: p:otrabanf itllf Cl}tmc lmcc.l"l.c.oz:.a.c.crirq;.a.datuo:occa5oni cqu_ilatcri co<pciuuaramcft nudicta\J quimc Qfiu cirmmfcromc.liuu ~cro.a.c.mt que fubtcndt( \'Ill q lUll gulis pwtason! plCdicti:co ~V arcus.a.c.cft t!uc quintcpartio circumfmntll! drl culi:oico haq; cp quadratll o!Jarumlinc~Jrum.a.b.'l.a.c.pariter a((cpHl quinCttl pblmlimtlld quadmum lincc.d.c.cft cnim qquarra fwmdiquadrarumlincc.c. c.qnadmp!umadquadratumlince.d.c.£umauron ansuluo. c.a.c. fu rccttJGO: p1ima parrc.Jo.rcrtij.cnmrq; qpam\tima pni11i qnadr11ta t>ua;: lmcannn.c.G.t tt.e.quadruplum ad qnadratum.d.c.isirurquadnua :rimnlincarum.c.a.-..a.c.-;: d.c.qulncr;plum funr adquadnuunt hncc.d.c.'lquia q: tlccima rrcdcdn nhb:i (lt dnmnn.e.b.cft cqualc qmtdraris oumnJt linurum.a .c. t. d.c. (cquirur vt qua t XIIII dmra·b!Jarumllncarnm.a.b.-t.c.a.rintquinwplllrn ad quadrarum.d.c. quod eft ptopolttnm. aJJ/:;)amfeftmn ell ct:"50 g> quadramrn I<Jrcrh; cubi atq; qn11dranuu latcnr. ~gnrc ~~~~1.'~1111 bafinrncutn rubnm 1 tignrd tmodcc:hn bafui. ~adem lpcra. ~lfCIJ~cnb.irltn.Jbo qn,ll~rllra_par!r~r acccpm quincnplmn June qu-adnm mcdtcmna Ot~mctn ctrcnh qntarcumfcribirpcumgoJ 1111111 dnfdcm figure ouodcam bafium. Cjllnd COJldariii vcre manifdlum cfl:contlat cnim ~danonrlmionc. t7.trcdc cimi !ib:i q' latua rubi fubrcudiwrangulo poJtogonl ouodcccdti ann cubii 1 o 0 dcccdron \'na c-adcmCQ fpcra circiifcribir:it-aq) e bane quanarn fine obicc contlat (o::darimn.'X. · 1i!>l0pofitio .,. r~'!r~~~~~~a~~~~:~~~~~~~~~;[~'c1'r~;~rfr:~}~ ~g~; cmqjd.-culodrcnmfcribuuntr. Sit fpcra mhm of:uncm .a.b.cirnlfcribcno: tlll!lil folidoo fil)ilra!i: 'iclicctouodcccdron rufus 'nuo cy ouodcrim ponagonis fir. c.ct )'(OCcdron cuhm ~111111 CJ. 1.o.rrfansulis fir.d. pcnrasono oti r .c. 1 trigono.d .Cuper ouo ccntrll.d.'l.c.circumfcnbanf ouo circuli buic <]d( .f.C.rJ.• 4·l;rri l!!i M"O.f.d. q ·5"· eiufdC:orco ft11q; 'l' bl t>uo circuli (pcra;z ,ppofi!ll;t quorum 11\rer circiifcrit bit pcntosomi.c.alrcr vcro trisonum.d.funt cqualw.Sisncnrnr cnirn ono latcl'lt pmtagoni.r. vmi c~ fnill anguli a ci'itincntia lilfcrio:.e. f.t.f.l).'l p:otmbanflinca c.g:.quc fubrc11dor angulnm.r .... femidi:trncrcr circuli que fir.c.f. vmiq6q; c1taccrf buo l~l)on! .d.f~S~Icf lmcris. k. b:'l p:orrobarur fcm~diamcrtT fui circult_qnc ftt. d. 1\..odm!C fumqr ltnca.l.nud qua fir hnca.a.b.quc c oiamcccrfpcrca1Ttgnatcqni Cllpla i potcnria:i] quidC.I.m.oiuidot i.n.tim p:opo:CionC balxntcm mcdiii ouo/ q; c:ctrcmil firq; maiol po:tio ciuo linca.l.n.-z rctim qu5titatC rotiuu. l.m. !lnccrur , ·~· ~iJ Cfrm:uG.p.q.iraq; fcmidiomcrcrcirruli.p.q.fit cqualio lincc.l.m.critq; 'J' conda 11 ~~r· :~;~~~~~~::;~::ii1~~·;~·.'t::~~~:~~~~0!~~; ~~~~~~~:~~~:~~~dd~~~~~i~:~ >-----.- -,,- pri:i~irure.J:. t•.qnilrri infcriba[ pmtllgontiO cqui!atcrutl circulo.p.q. miull \'nurn ' lartktfit.p .q.critq;c~. ~o.tTcdccimi ltb:iquadrarti.p .q.ctlm!lcquadratil;lOmmuu lmcarurn .l.m.oz.l.n.ParircracccpthJ.con!huantcmc,J:O("monllrorionc.1c;:.trcdo cimi~.b.k.cllcqualia.p.q.crsoqnadratnln .b.l;:,c(t cqualc quadratia ouarum lincar>.l.m.'l.l.n.P.ircracccpria.St ~croc1t'(tn6flrati6c. t7.f!Cdccimi.m:mifclhi C 9'. e.g. C l11rus cubi o.b cadC fpcra circiifniptibtho:(jrc P. cond'.t4.trcdccirm.a.b; tj C OiiJmctcr (perc potcutialiteri rripla ad.c.g.q Claruacubi.O arit.c.g.olnidarur Mn ,ppouion~biiton mcdiii oooq)qtrcma P) c;c oononllrati&. t7.trcdccimi cp c.f.C ranli; tnaiol po:rfo ciua::lgirur cyfcruud~ bui9.c.g.ad.l.m.flcur.c.f.ad. l. n. nam ~t rota ad roto.lll fie malot pouio ad maio:cm.1roq3 pcr.lt.fl)ti quadrotnrn ~-S.I!d quadr9tmn.l.rn. ficnr quadratunr.c. f.ad quadr~tii .l.u. i]rc P.·• J .quinu q 1 dr>1ta omarurn lincorum.c.s . .z:.c.f.paritcr ocup1a adquadrora ouannn linea rum l.m.t.l, n~P.itcr acrcpra ficut quadratU.c.g.lldquadmti.l. m. ers;o P.· •f .quinli:ct