Elementa geometriae

Page 102

LillER gtdi trfangulo;: p!ramidC circlidliriti qui fuplat~a bafw ipfi" pir.tmid~g~6f•flunt. p:mrcr "cccrn fult miU02Cil rntuiLbU'JlliiSUho bafN l:ucr IHCcpUil Yt cul~.krcr.cont flat c.,: p:cnmf11 rom'squot ansutoo baf11.1 _bllbucr~t rcpcwa.adbuc •.lccc!Tano fct quirurc~ c6i fd:a fu~ftct>~lc:.la ns;uli.hl ~oh~ulli1SU1u .'3. _conuucmru ~~ucr ampr~ dfcnlino:ru quaruo: rccrt11 :co mqua lllillOlCO" quo~ llll!)uh msono;zptram&J dan ctrciidJ.IHllllllqui fLIJ~btcra bafu31brutc p~ron ndti.l coufLtlaL\[ CJ.:ccdunt oi11 11Cccproo. 1i!::l2opoltrlo .:u. ansuU lilpcrhcmlciJQU01! quinq3 ·ouo p3rircrac1 crno tint uaaio:co cuncw;;tibi imnccm cquto lmcta . iUOlHJb 1pf11¥ li1 tnangulnnJIIJllfli C.5mt m::u fu pfictalco ansulL.b.a.c.c.d .f.b.s:n.~r,pponif:tllks \'ldclicct ur qui q) cuo ,01u; r~iuo lmt IUilLo:oo .fimq; fc,: latcrll coo commcnltll cq~mlta. que lull o.l.l.Q..c.d.c.d.f.g,b .:s.k.'< fubtCdaufdomobllfC\lqucfuH. b.c.c.t.b.k. £Jbt:J cr£1otrlbuo b!lflbuotnnuguhi 1\ioconfhtui polk.fftocniangulu:J.b.a._.t. c,luat Uoongulo.d.'l \UJC<J.o.l.lmcc.d.c.'lplotmbaniUr.l.b.t.c.cru,l) CJ.4· p:t:m ~IIC\1 t.b.cqualia Uncc.c.f.c;c ypotbdi 'fl'TO :Jitat totakman~;ulti.a.Cilc tnatotctn 1\ll:ill 1o.s.cr11nt cni quiq; ouo q: tri~llll ousu\tt,;.b.a.c.d. 'l.g.renio nnio:ctJ 151f q .. t -4- t ~ ' p:inll bnC\1.\.C.hllCJ.b,\U 11111\0l.CUIIq)fUII CJ,.:.O·p!lllll ouchno:.l.b.'l.b.C.IIIJ10 W rro lmca.t.c.fequuuroulo lincao.t.b.'l.b.c.CifcmultofoJtin~J IIIIliO:culincll .b.k. , quia i~i ru r .l.b.ctl cqmllt\).c.f.crum ouc hncc .b .C.'i" .c.f.nmo:n; lu:cc.b.l;. [on I llar ttllq;Cocmodoqulfq; OU>l\J lincJIJ ().:tribml llllciu .b .c.c.f .tJ .\;. clfc longtt oX\1 tcrtta:i~tf c;c.u.plitni couttat \'CHilli clfe qti oimur:boc oii tll).'Qt add1to 91 fi ouo ansuh.b.a.c. z.d.patircr llCCcpti fmt cquak\J ouobua rcctio crunr Otc hncc t.a.1.a.c. c;c. ,4.p:nni ltncol \'na:quc cum ftc equalio. q.: ypotl;cfi ouabuo lium.s -, , ~ b b.t.g.k.qucq:.:~.o.pmmlonsio:rofuntlinclill.b.k.cunq;q:cadChncccuc.l.b.-..b _ c.fint lougiotrohnea.l.c.fcquitur vt puuo.b.c . oz . c.f.c•r~r acccptlls cC tvngiC'XS b.lt.i\t vcrofi ouo p:cdimausult fum maio1c1J ouobuiJ rccnu:crunr q:.l •. pmnt 1:1 ouclmcc.a.\.-..o.c.idcoq; 'l duc.e;.b.z.g.k.b:cuiolctJ ouab9 ij ftit.l.b.oz.b.c. qua rc ~r pliuo.b.c.'l.c.f.pamcr\lcccprc funt lone;io:o:; linca .b.l>. . ' 6M • f ' 1P 1opolitio .2~. 1tdmo :mgnlio fill~fKialtbuGp:opoltriG quo¥ quiq; bnQ P-ttcr accepri tcrrio timr 111\Jto:cG unmc.:Hmt rrcrumul qua mo1 rccno an;3ulio mino1co:c~ rnbns tills cqmllab'' qua lc!CmJq) run roiidumansu tum conliJtucrc. fiSmt ,.ppoftti nc01 ansuli fu~tcilllc:3 qui fum.a.b.c .oc tribnll illi~ cquaUbuP ~olumno \'uii folidti atll)Uhi conl tnucrc opo:tct: •s•f c;c . 1t.l)~ \"'tlltllq} ~.:.~uo co:;;-parircrll(ccpti rcnio fint maio:aJ: 'i" CJ.lt.buins \'t OIIUIC<J !;iter acccpri quatuot rcctio11ngu\to fmt minoteoeJ ipftsltllq) fun bee pofita:btwa "cro coo conrinitill cuunaadinniccm fiut cquaha cwq; fubtendantur trcobafro -z ipfc fmt d.c.c.f.d.d.critq; cy.p1ani1Til poO"ibtlc oc tribuslindo biu baftbno cqmdt~9 ui ggulnm con(litui.5u tgtf cr. ctu:c6ilitut~ filn ooctriJ J ~ . :u .. pmni triangu:uo.d.c.f. conftitutuo: cui fflcur oocuitquimaquarti Qrctifcr,bai nrml~o. d.c. f.fupr(l cent mnn .l§.'l.plTilb~f:l).d.g.c.l§.f.que cti fiiH adiuicC c~kll t,: oionc circuli blccr.Jq.J XII rreo ,pro~ roo an15ulo~ arnb~aJtlll cqulllia q; ypocbcfi ttcccnc eft vr 6:1; qu l"b quohbcr tllomm Ia rem f1r 11~111?! c~naiC a~ir aut lll:lio:i cilc ell impofftbtlc ~~CI~~ ltnc.t cr.!cntJ II ccmro:s-~d.mcufcrctiiltll ormli.d.c.f.CITa cquah,; ahrm btqz.a.d 11.c.b.c .b.f.c.f.c.d_.fulll~~Lmr pzoprcrc11 que pofua ftir annumre .s.p:iml rrc!lan guloJ.IJ..~.c . .ppof•rao clle CIJU3lcornbuo lllli)Ulia.d.g.c.c.g.f.f.g.d, Ctiq; bi m:a f~nt cqu~.e\3 t~latuot rccrio ~:u:guht~ vr fuctk p; ct.1 J.p:imi:p:otrorta pauhfp vua hnca¥. eJCtJiiu a wmo .~d cim1fcrcnti~rn 111 conrmuum oz otrcctti:cll"cnt cui trciJ augul1._a .b.c.cquat~o au _quamm rwteqticil c6cra porn a. Qtif1 e!lCr maio: fut pcrpofu!o tnbuo rru:mgnho quomm funt llii!)Uli.a.b.c.tniJ9 trl5:;ulio oimdwtit busrrl:mgulum.d.e.~.vnoquoq;tlhciiquoc6tcarmbafilla(}'bafcll fUllPOUilllf ~ b.Jftbi!O: cqnal.c<J ~•dd1~cr cqnahbuo-; ~nguli.a.b.t.cadam ad 1~wn puucii. g. fcl ~cr~r c;r.:~.t.~\11 rr~_snf5u loo .a.b.c.cllc maio:cs rnb9 qui fiir.d.g.c. c.r.s.f. g.d. C'11t u~q;m;no:co_ qruot rcmo q~ C atnph9 :JIT_>l~ti poriris 1\:clinqmt irllq) vmi/ , . quodq> cr. fc;r l:ltaibuorrcv ,woruoo a nsutoo ab1cnubno m11m~ Clli: I mea ~rcdi ~mea ccnrro.g.ad m_ctifcrcntt~.d.c.f. idcoq; cUd vorcntmo.5it i_girurpormtiuo I hllCQ,g, ~.q_uc fit fctllll. 1 1.b ~ OllbOSOIIIIhtcr CTW\l fill? fll~~fki( lllll)Uit fci ctrcu\j d.c. f. ~mltrllturq:, rrc~ rpotbcmif~.ll .d.b.c.b. f.qua £J oico c6nucrc anguloll rrco f~pc~tctalco cq~talco niDus p1opofuiu COI~iiiiCIIICt> aunuhi fohdmn in puncto.b cu em qmtdram huc~.a_.d.ftt equate ouob quadrout) Ollll¥ linca;:.d.g.1. g.b.cy. yp~rbcf1 Bt quadram lmce .d.b.f1r ~qmtlc ctfdCc;c penulruma plimi nccctTe eft Iii n~.ll.d.df~cqualcm lmce.d.b codiq; modo-zhnci.ll.c.lmcc.c.b.igif cr..s.Pmi (II b:lfcacua ftnt~Uillcs cntangului.'.a .cqullho angu\o.d.b.c .ftli'quoq; n6cnt at ~h~i).b.cqual!u angulo.c.lJ. f. 'i" llllSU!oo.c.cquahu augulo.f.b. d. quare cOllar facruccquod fBcc~cOi fpofuimuo. 1/b2opolino ,24. · c6rin,arnrciul." 'lCquidillanriii con!cnrum ft~pcrfiocb~IG p~tn~ua t;cccff< eft cOr men: que ftcut c~ . pollunt pa~no:cv fCJ ll!l poll lull dfc in omni numcro part fa n~nmn c~catenrc..Co_nlht em colmnu.l c:cagonil polk s.fupcrlidcbuo que binc~ bmcoppofttcflbtmutremcqui~ilhuucommcn: fiCquoq;oaOi!Ortj, 10,-zocragot §) nam. •l :'l ad tlt11,: fumhrudmc m ~nfinini. f; bo,z omnui folido~ cquidllhmibotJ // fu~crftctcbuscomcmof ~lUC_ m~mra ctTc p:onuncio fohi ttlud OICI{ p11ralcllogra1 mu CUIU:) Oinno.> fupcrhuw apfu_ ~miJiclltc.a paldl_osrat~.c fum ttftud fc,: fupcrfl acbns ?Ulllll_Jilt needle dl am~m;oc r~!J it!lq) qofcJ tm flll~fJcicbuu ambi{ OI(O !Xbcre HCIIt£11 '!P bCC.J.4.,pponu:fic iglt talc .fohdum CO!puo.ll.b.cuius onmmo rupcrfiCtco fuc_ vt .rohdo bab~tu mente c6ptebcndas:p.Jtcbtrq; ttbi mlqu~q; cani Qtmm~: CJ rchqutu fcrorc ruumquaruollatcr-.t cum ftnt c6mm1c~ rccrtonc<J ipfwtJ feu nus -z~qm:u_uo: fccra;.:.Sim aurC illc q1~atuo1 fccrc binc oz binc funwadinulcan op~uun_r ~qmdtila.ntcs c;rypotbcft:fcqmr c;r. t6.bi~ ll~utnprllut quolfUO"l latera but _fuQfit•':' f«llllll!\ 'l quatuo: fwa;z fmt lldmnicc bma 1 biua cquidtllUria. £6 It at 11a~; fcen~. Be \'cro c;r.J4.plimi mamfcllii CoiallltcrB oppofm1 11la;z fc,;fuP. fiQqzcccq~•·~ha:enit ~gif"bh~ll.btcra_ansulii pla111i cOrinCria miufq; Cll:f cquah9: ~~~1lo ~arcnbnu llngu!u pl11nu m fuP.ficie ftbi oppoftt~ ?rincmib9.1lnsuli quoco ab 1U11.1 bmio ozbinlu tarcribuu ?tcmi cqulllco ~.,o.b": 15if q; ?Ucrfa pcnqlrhnc ro1u