Elementa geometriae

Page 121

Lll3ER cqua\io ~lli)U!o.a.c.b.it~Q.)Pcr'C&m fciom ans~lua.b.tota\is eft rqu~li~ \'ll~n~o e.rotllli rrr:'.1CIIi partiJ\a' an~ II c6poncntr<J ~nu fum ~·}na~ca tnbu:J v.ttoltl.J. cot ponmribu:J a!imn ~uu(quifq; fuo rdanuo.VfJoamfdln c tSU!n 9' t~roon~u!t.c.b c. nO c61fnucfu111pti i11 ~nopofuo pcnr11gono fnnr ClJUaka.cu aut f1c ocmo11 ratu; dt tomm pc1 •rauonU dfc cquianguhun vrrohl'oct.cr:3o. m..o do conllllt p:opofuum. hlrcrclito·quadnuii 0c1 · Oi'Jinctri circu!ia ,qq: :~;;~;;:~s;,~\~~~rr~;~;;;1; ~~:;%~,:~.~a..bi~.c'!.f;u:,p~:naacncsnutmu1i..dl. q.ou.Cb.acd. libli'Zplonabafict cooiamcrc:r.a.d.e olcocr<oq•q•>adr,u;.!i''",',·''m·",.':•".'c.'''r~"uo·'r"d~:at':~~~~~~~~~~~:~~~~~~;~.;:~~~~JI~ n n~u\no.b.a.d.cqu J liollii~JU\o.c.a.d.qn:m: per vlrim j fc~i a~·cu? . ~ .c .ell cqualiJ ~ncui.c .c.ft q1 q:.l7.[CftiJ tre~Jarcull.a.b.b,c.'<.C.a.fun~ admmcc cqnakt> co q' co;zcbol\k qUe funt la!Cro trigoni ~tit cqualet>~ tyorbd't :cri.r arc~IG.b.c:fc,:ca ~ ciroifmnuc.idcoq; cbo:da.b.c.cm llltul' ()11!§0111 cqutiJtrn tpft amJlo !ltfcrtptt. qmnc per co::cl'. lf.ljrri lincll.b.d c~li<J f.:midian~crro.a.d.DI31lnifcp? CnmC ~ ptlnn parte. ~o. tCrliJ cp anoL!Iu<J.Il.b.c.dl ~cc:us .tdcoq; quGdr~J.IIlm :lm.cc.a.c.c cqu~l · quoJdraria OU>l;thncll;:.ll.b.oz.b.c.r.ttcra((cpfio e,cpcm.tlruuJ pun. :Bt vo ro quadrau'i .a.c .quadntplii ad quadratum.b.c.c~.quartl fctit ..cum hnrl].\1, c.ftr tlupb.b .c .rclinqulrnr ergo quadrilrii. a.b .lriphi cflc .. ad quadrarum.b .c.-: tck.J ad quadrarum.a.d.qOctl ptopofilllm.1161JIC'Jt atirnoJ <}' l inC'J.b.~.qnc r IJ.rth3 tri soni oiuidat fcmidi:unc~¥·d.c. pcr cqnalia.-ffto.quidO: punCIIhJ ounCionh,.f.con/ Rar lgtf q: quarra pmm ~V .b.f. dl cqualt<J f.c .tdcoq5 per p~mam pancnt rem~ rcrnj omncuans!lltqut fnnrnd.f. funr UCfi. qn:mc,:.pcmdruttll p1lmttwadrotu .b.d.C cqn~lc quadrarill ommnn liurorum.d.f. 'l'. f.b.quadmtum ~cro . b .c .CC\U~k: quadl'\tltis ouQrum L.ncannn que funr .b.f.'<. (.c. fr qt.b.d.dl cqu::thi3.b.c.cnmt ~comuni frlcncia ;:,uo quadr.JIIl ouanunlincamm.b.f. t.f.d.~;itcr llCCCPIIl cqu~ li:( ouobttl3 quadroris OUJ¥1inca:;z.b.( • .z.f.c.pl1rircracccpriB:ocmpto igif urnnq; qn'<ldnuo .b.f.crirc:rcOi fcia quadwmn .f.d. rcftduum CtlUilkquadrnro.f.c.r~t Ciduo qnarc t 1inc11.f.d.liucc f.c ~bac c6i fciCLitia qua;; quadrnta ft11 cqu~lia cas lin rood cqualct.1.f,: boc traq)manifclhl i ~ pcrpmdtoibrlo OUct\1 11 centro ctrcu U oad latus u;soni cqui!arcri ftbi infcripri cquahtJ C oimidio,,incc ounc11 c~:rro ciuC dC circuli ad ipfino mciifcrcnriam. 1~1opolhio .'). 3Jiams cpgonicqutl'ltcn lamli.1~ occasoni cqnilatcri quoo'Jm~Oll\1111tllidCq,;drcnluamciiiCribirfibt mnicc; in IOgii Otrccriiq; cOiti~'lnf rom linea cy do cOpoftm fm J'PO~tion( b'lb~rC mcllni-;:;uo C}.'trcma tiinil~t crit II HII io:q;,ciua po~no lanto r}.'agoni.fi6 irctrwlull .a.b.c.wum cammn .d.1 oiamcrcr .a.d.c.filq) arcuo .c.b.qnima f!tlllfCIW Ccmicircuh.a.b.c. mi fubrcndaf cbo~t~.c.b.qui :'lbt dlc lltu!J t'CCagom cqmtarcri ,ppofito cirwio Mcriptt adiungg.fq5 Iince .c.b.imO!inmi 1 oiwlii linea .b.c.quc !JOLI~t urc~; c~j l liolarcri c~~oui cquihltcri i)dtc1o modo infcrlpli oico rotci lind. c . ..:.oiuifatn ,,; in punao.b.t7m ,ppo:tiouCbab,mC mcd1ii o; cuo ~trent(!.-.: m~aio:') e~9 po:uouC XIII <Ji~o ell'..: linc.i.b.c.qncdliJtns (JoJgonl:onront ..:ni in crnr;z cnctincc .c.d .... b.d. c.nrq} 11ngt:h1L1.~ ·,c,-:mth o an~ulo . b.d.c.ey. r .p1imi ,pprcr boc cv linea .c. b.C ..:~lfEJ hn~c.b .d. L~. !Ol.d • • ~. qt t:m.t 11ngtJiu9 ~uoq5 .d.b .c .eft cqualio angulo .c.q:. 5 .p:i nn.qnl rcc~. 32.p!llllt llllgui 1 .a.d.b.cnr oupluo ad llnguhi.d.b.C.'Z q: P- cjd(an 1 ~~~~~"':d.b.r.c. tmp~!'.~l ~d ~ngulii :c.f(4111f "ronguhta.t~.d.b.flr qnadrnPl'J ad an/ snln.l.£tl ern (1: cot fcta <]dmp.l~ quicqULd fucnc ouphi oupli.niq; fir Cr id.:all\i\1 lu9.a.d .b.~ht.lruplus ad. lll1JI!.u .~.d.c.cy "lruua fc;rtl co <}'Qrctm.a.b. ~:quadm ~1m;; ad ~~cu.b. c .. uccctT~ c c.t em fclll_ur anguhhJ.e.fir cqu~:is lltlfill:o.b.d.c.fllgif t~l!cUlJ>Jur ouo lrt\lll:)Uh:d.c.c.rot'lh!J.'l'.~.d:~·P.tra~iooi an~ultto.c.roralis ftr cq ltoan.~nlo.b.-d .c.paniahu tanguln~. c.ftt rotavcnufq; uccdTcCc~. p.p1fmi :vt I~!• futt c~uta~lgnlt :~J:l!C per 91~ana fc,:ri ;ppomo OUOf tarqt.c.c.-r.c.d.c6rincn • ~tn ~ns;ul~1 .c.t toluh.rn?Bulocftmr ono;:latc7- d.c.1 .c.b.;:niuCriti t1id.:ansulii •t-----< 1 r.nalt lnllll~u.lo qma li,PP?!t!o.c:c.oad .c.d.cficur ad.~.b.c;rfcOai!r"?.l'\llitlli.'Z d.c.ad. c.b.cftcur. c.b .adcadcc,:pma t]tc dnfdon.fcqmi'c').c•.C'Inintt m ftrp:o P~lli?.c.c.od.c.b :fm!r.c.b:~d.b.c:.illllnr 11 oionc c&lndc ,ppofu1i lmc.i. c.c.ciTc Otutfu 6nt plopo:ttonc ba.bt.'rcmcdtn 1' ouo c~trcma-; maio!C po:tconi duo ci I at tu.o CJ'~I)OIIi ~ Ol'u:ruitno-.:; ~~~~nfinlt~.£0ucrf:lrn quoq; ocmoullrurc;'ncnit qtl flctlc ftcr \1\1 rcrrograda:c~t 011 affmnu 'j)tolcmcua napitnlo .9.ptilllc oict!Ois oalmllg~i ad ocrnonflra.ndt! quamtr~rCcb~:dap amni circuit . .Dtco irt~q) Ql fi lit uca qudtbct lim ptopotltonc babcnrc mcdm 1 onoc;rrrcma oiuldaf cui no circuit maiot po:rio fucrit Ia ru~ ~.ragon i:cinfdC mtno: crit lawo occasoni. tit ~cro wino ntinot crir.lu9 occagot.Lt CLnfdO: maio: em latus cragoni.Sir cni p:io:i oifpoftli6c mancnrc hncil.c.c.ollltf.J m punno.b.Mn p:cdicrd ptopo1tfonC1 maim ct9 pottlo fir. c.b. Oleo 'l' minfniq; circuit hnro.c.b.dl !at" c~agoni ciufdC ( linca.b.c.latull tlCC'.lSOt.li:-:: cuinfcunq; circuh linca.b.c.cfl lltull bccagoni ciufOCdl!inca.c.b. IJt"' CP\10111. 3nrdligo aiir boc occNsonto -z occagonis cqnilatcrfg.fi cni fit.c. b.lat lull c~llgont cirmlo.a.b.c. infrripti:crir P.Coucr. t f· quarli .c.b.cquaUa.d.c.1 quia ,vpoltio.c.c ad .c.b.ctl fimr.c.b.ad.b.c.c~ypotbcri Clit c,:.7 .quint!. c.c. ad.d.c. fimt .d.c .ad. c .b.l~i{ c,:. ". fc~rt ouo t~&nsuli:c.d.c . .z.d.c.b .fnnr cqui11ngnh :angu lt.IO crgo.~.c1l cqt~hll augulo.b:d.c:tpfo<Jcml~rc:ro ,.ppouionalia rdpiciuht.niqs; ftran sul .a.d.b.qdmplusadagu.lit.c.q:.Jz.!lmbioa!TiiptQ.tquitaciufdCbis: 0 fcqu i[ vr cuj idC an~ulmu.d.b.ftr qnadntplull adanguhi .b. d.c. idcoq; c,: vlria fc~u arcno.a .b .quadmplua ell ad ami .b.c.tmca igif.b. c.C tatuo occagoni .a .b.c. :~r~:;~~.~~~:i'~~~-~~;~~:~~~~~,~:~~r;~~;~:~~~~~~',i~~:~:~·~:~~~:c~~~~; , ciufdC. inrdiigaht igirurinfcrtpri cC occagonicqmlarai ouobno circulit~.a .b.c, 1. f quo;: ormJilli latera cnit cqualia hncc .b. t.'l quia oio figura cqmlucra cirrul.:~ tn 1 fcrtpra c equiangula \'tpwbarii ell. Ul . lf.quanf lib1if~ uii' vtrofq) t'CrugoUOt1 cnc cquit~LI~nloo . .(nnq; ormrc<J ~ngult .vm9 ~~ rcr acccpu fmt cqualco onmibu9 11ngu LlJa!rcnus paritcr 11cccprW ftrut cutdcnrcr Apparcr c,: ocmoullrati~ in. Jl.primi: nccdTc C q bac c6i (cia quoniliba cqtui occimaa aur quoranibcr prcn cinfdO: ocno tarionie: cC cqualro ur Vltue: bo;z occagononi fir cquit~ngulull a!ii.lidcoq) fdlsc,: ~one flllum CuQficic;z:-z~ fi ~ftsurc fill.:s ouobuo (!fat lis mfcnbanf:ctir ;ppol no ouo:;z rd11tmo;z larqzllla;z fts;ura;tfic t oua;z Oiamaro;zillom; circulo:um vr appgr~t q;com:t',,s.fqri libli 1ptima. tz.di latCN occasono;zftliunt infcriptOlli P4