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Show a"- "-53.5 1., ‘ 136 EVCLIDIS ELEMENTORVM PROPOSITIONES. & maior portio fitl n . angulfi d.vel [up 52" primitSc quadruplus ad lm quod critlatus hexagoni : 8; In. Iatus dccnqcni , in circulo p q. dcfcriptpmm 1):: [3.5 prxmif . (lglrcquadrutum larcriqu. puntagoni {cilicct in ipfo circulo p q. dckripti, crit ! mqumn quadratisipfirum l m. l 11. per 1;" angulum b c dpcr vltimam {ceridco angulus d.Vcl b. duplus cfi: ad nngulum b c d . (inure angulus b {dipfi d. angulo :tqualis duplugcflz ad angulum b C (1.86 per 52" Primi, ad ipfum Prrcccdm [is . Pcrcorollarium autcm {ccundum rcgcritionis , I1 k. lzrrus icofahcdri cl}; xqualc ipfi inuiccm mqualcs . (Lugre liners c f. fb. ~b d. inuicum xqunlcs. Cumdueipfic FCC diunfia: ficinnt dlrplrlm ipfius c c. 13111 & 11)in b d. c d. {imul fumptre facicnt Pq. & idco quadramm ipfius 111:. err: mqualc ' duphmr erufdcm c 0. Ergo 85 dimidia ipfnrum b d. c d. coniunéla pmmlfl‘lqurilcubns diam {P1133118 infiribirur Psr VLim um corolLrep ;ritionis. Er fl :3 gfccetur fecundfim cxtrcmam 56 medium mtloncm : maior portio erit cf, pet < m} r) n A.T A , (Juod i1 latere pcnmgoni , quodfilue ex eius angulum quadmmm ipfirum 1111. In . Scd a b. porcu- tinlirzn' :ripln (ft :1 d. c g. latus cubi, par 18"" fubtcndetcdumd fumpm,quincuplud1 fimt qmdmti, quod ex‘Eirculi I 05 prmmlm . Ergo per 7‘. cmfdcmdicut c g. ad ipfum 1 m. fic c F. 9d Ecntngonum c1rcumfcribcnris flmidiamctro. Sit a bdatus pcntmoni ipfam 1n. ‘c.l;1t.usdccagoni: b c. {ubrcndcns angulum pentaooni c d e. dizdlbctlr (ligartpcr 2.15 fexti,quadrntum ipfius c g. ad quadrarum ipfius l mflcut quadmmm ipflus c End quadratum ipfius l n.Et idco, Cll'Cllh a 1? occmrum autem d. Aio,qirbd quadratilinearum 1L1) bLC Per 1 3i quinri, ficut aggregatum quadratorum e g. e F. :1d aggrc-gamm fimul qumcuplum facrunt quadrati d C. vcl C d. (lgéodlic oficgdigur. ‘ quadratoruml m. I n. Iicquadratum ipfius c g. ad qrmdmtum ipfius 1m. Et per 155 quiuti,& permummm proportion:1n,trip‘:11m quadratorum cg. cf ad aggregarum quadrntorum 1m.ln. ficut triplum quadratiipfius egad rriplum quadmti ipfius l m. Triplum autcm quadratiipfius c g. cfl: quadramm ipfius a b. Per 18"" preemim . Scd quadratum ipfius ab.quincup1um ad quadratumipfius 1m. Ergo triplum quadrati ipfius c g. quincuplum ad quadratumipfius 1m. Qgrc triplum aggregati qu'adratorum c g. cf. quincuplum cft ad aggregatum quadratorum 1m. 1 n. (‘36 ideo ad quadramm ipfius h k. Dd 6.1 [341 C. y [in primi . ~Clc.c- D-C b. [1d 6. [Id 6. C] b . 3.} y 13 5mm: [3. d 6» Ed 6. D' a b' Hlnc manifefiu m CR, qubd quadra ra,cx later: dodcahcdrl & ex Iatcre cubi in cadem fphxra locntorum fimul fumpm, quincuplum Faciunt Etr- quadratl, quod CX {cmidiametro circuli pcntaé/b goprrm dodecahcdrl circurnihr-ibenris , fit . Nam fl fphtra circu Icrd‘ut dodccahedrum & cubum, latus dodccahcdri cum fit 4 b "'1‘ cub1 lgrusg b aficut In 20‘ prmmifli, vcl per pofiremum 11 :1tinm . 61'" rcpcuuoms conffitir. core 31 Sitéuc circulus p q. cuius f‘ernidimnercrfit angulum fl) c: ipfi igitur b c f. fb C. angnli facum xptmm c c. ficut proponirur dcmoni‘trandum. 30 I37 1) f. & quonimn angulus gc b. duplus aft ad _ I u 1»: yr gnculus ' ' ‘ ndlt ' dodccahedri cgmprche quin mm7 1 & loofahcdr m1n cadem _ ~ ltrmngulu . . fplmn~ dcfcriptoru m. gfi‘om ‘ puflim 1 €111}13_(i1:1r11ct_cr ab. Cla‘uh dodecahcdri bafis c. 85in e d f) 13",, Scfcrlptrlcofaheriri bails d. Sintc'lueha: :1 cm Pm" [ICE bites ; mrm ' " cuculos cf g. 8: h k. a b quoru . m \{'cmidilmetcr c f. d l'x. ccntra Cd f . ' 1"' ff ‘ Aro, quad mqualcs fimt cf. dk. Si. 5/:\ cmm a b . potcntialircr quincupla ad £\ gyiazmd m . (Lure in punflto n. {eCcrur \ gcudum nudum 8c exrrcmam rationc'. "1 C l quinde- Per I 5"" muem pra'mim, quincuplum qmdrati iglius 11K. cuplum eflt ad quadmmm ipfius d k. & last 3 LL" huius , triplum aggregati quadratorum e gx: F. quindc‘cu plum Cfl ad quadrarum ipfius c?1raque quindrcuplum quadrati ipfius c f. :L'qunlc CR quindccuplo quadrati ipflus d k. Igitur undram ipfarum c f. d k. {untinuicem :Bqurdin.Et Pcrind; inl' C Ed imquales. 0\ugd fuerat demonftridurn. PC R p E "N D 1 c v L A k E s 2;. Centre {91mm ad bulbs dodccnhedric‘k Nnmque icofnhcdri ab ipfiz fphztm circumfcriptorum 111m nequllcs. bafc‘sipl'as circulorum huiufinodi pcrpédicnlarcs cum {cmidiamczris acicircum [Lulu-n tium & {Emidinmctris {phnsrx ad angulos bnfium larcradl‘ilicct mtis fixciunt trinnguh reckmgula . In quibns cum duo {Pin-rim {cmidia metro,& duo 1;1tcrn,fciiicct {cmidimxctri circulorum cruntptjt bail-s (:ircumfkribmrium, per prrcccdcntem fincz'eqmiiu, , inuh pcrpcndicuhres {cilicet latera, Penultimam primi : duo rcliquu ccm quoquc azqualiadlu‘ut of‘ucndcndum ProPomtur . cm». |