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Show ELEMENTORVM pRDPOSI‘I‘IONES; 139 Prafmifli, in b c. produ'citur duplum trianguli a b c. per 4.1" primi. hoccflidue inter, qubd ipfius hiatens cubic: medm & extrema ran-9n: dlulfi m.a:pr2CCdc-nm, ior Portio c& a b. larus dodecabcdncum . IIgltur, PCI7‘5‘ _ {climguod 1 Per , Fan" g, d m d1pfa ficut had ipfam a b. fic c~d.a fit ex h.in d gasquale CB: ei3ql‘1od ex :1 b.1.nlpfam c d . Scdpsrpnmam [CHLflCM C1110d fit 6X h.i,n 1191?qu d gad 1d',q}10d fit ex :1 c.1n1pfam d g. fir cx a b. fic eff had ipfam a c. Ergo em Ixcut h.\ad1PIam a c. {ic quadflum prxccZOIOHa PC'I'S en en " :ch? g. d _m c. a in c (Lad .id,quodcx triangula,qu:e {um pars 50" . fexagcnari'j: ‘ dcntis,fic-ut dodccahedrl filpcfficws adxcofdh‘edu Itlpcrficmfn. mum hcdria. ad [was eius b c. excat pcrpendiculdris :1 d. Aio, crabd id, quod {11b :1 d. b c. compréhenditur , cfl: torius dodécahedri [upcrficiei pars 30‘ . Pater. Nam: ‘ totadodccahedri {upcrficics difl‘écatur in 60.triangul'aunflhfl. {ingula & fim‘ilia ipfi a b c.trinngulo.Etcx_1 d. . ‘ ‘34 Q91) fub perpendiculari in ccntro blilSlCOfathri ad lagus (Sci-11b ipfo latcrc cont-inerur , rcéfangulum cfl torius icofahcdricz: iugcrfielfle pars tricefima . A centro balis icofihcdri e. ad lhtus. fg.cadat perpendiculani e h.Aio,qu(‘)d id,quod (11b c H. lgxfi totius icofahedri fixpcrfiari pars 50‘ . Parct.Nam tom icofahedn‘ fupcrficics difl‘cnlhturin 60. triangvdamquali.1 finguh & Emilia c fg.tri;mgulo.& cxc h;in Fg.f "17* g producitur ipfius e fg.trianguli duplhm. quodrdc (cm. ginta fufcipit parrcm tricefimam . Manifci'tum cfl ergo , quéd dodécahedri fitpcrfi'cics ad icofl1hed‘ri= fupcrficicm elf, ficut rcéhngulum qubd'f'ub late-re dod‘ccahedri 65d perpendiculnu‘ a can tro continctur, ndrcétnngulhm , quod {11b latere icofhhedri &ei perpendiculari é. ccntro bafis com ptchcnditur .. Pater 3, cxtrcmamfiuc mtioncmgpaimyprrio f5" d g.Ex 20- . 3mm ex przcmims 85 ex x 5‘ quinri. D o 0 EC A H ED R1 filpcrficics ad icofahcdi‘i fuperficielmcfi flcut cubi: latus ad icofahcdri latus,in fblidis {cilicet ab cadcm {Phrera contentisa, Eflo a b. quidemlatus pentagonz bafisd‘bdccahcdri : a c. vcn‘) latus trianguli icoléhcdnci in codc' circuloa b c.(vr przmiflh 31‘ . ofiendit) dcfcriptorum: quoniam {olida ipfa‘in cadcm {thra confined (111390‘ nuntur . Sintc'l'uc :‘a. centre: dad ipfa later; ‘ pcrpendicularcs d g.& d c..qu:e adpcriferiarrr produéta difiinguaripfilm pentagoni latus £1. ' f 'Tédcm 11.1mm fit latus cubi ciufdcmfphxrx. 1' Dem onflridum effiqubd dodecahcdri ‘f‘upcr- ficies ad icofahedri {upcrficicm eflt, ficut h‘. Iinea ad'a c.1ineam; Hoc modo. Nam d {an in rcéhnn pofim,pcr l 15 przeccdcnti {ccfidl‘lmmcdiam & extremam rarionem {céta cit". 8: ob rem Balls. fupetficics ad hanc, ficutlmcublwm latus ad lpfum a. c.. . ficur‘p‘ropomtur. icofahcdricum 121mg. angu‘lum geatggom E x dodmn tc diamem 1n dcxmntem 13:16-13: {ubtcndcmis fit azqualc pcntagono , quod a c1rculo curcum cu "It". teaanaulum. Efio in circulo a b c. pentagbnum zlequdatcrum al- c. m angu urn vbi ccgtrum fir d.diamcter b d aqump a b.1mca funtcndc ltflun glFof g. o punét cntagoni ab cfccct 1n . ubd ex :1 h. qua: {it dcxtans,hoc efigxg 111‘s :1 c. tuin b Equa: dodmns 6Q xpfius b choc :fl: 3 Pxo 3 cifur rcfiangulum :equum ageq pbngagonl$12111 ab C. Hoe modo. Per 4? . FY1111}, (1110‘l .tcx a b k £11343, b (Lin :1 g. du him CR ad tirlangululm . a. quod fit ex 3 f. in a g. mplum trmnguh m gulu trmn ad um dupl qlrodque cx b f. in gh. m a b d. @rc quod H: ex b f. in a h.-quincup1u , ' pentagono z ficu t dcmonftran.‘ ' o xqualc‘ ton . au-li a. b d. 6:1de tri'uw hdrilams , EC duals/"divu ofiendere , {luéd flcur cubi latus ad icofit fpal:1:ri;: e:d<im} 'T gdcm Q‘Pfl edri fwfah 69: dodccahcdti fupcrfides ad dtur [1151:4011 :1 :1 'q E: ad dcntxs pracce m iptio Dcfcr . rum confcripto o ECa c r1. b k l. Eritque pcmagonum a b obsirs lpfius c la locst?n'unti {phiier gndcm in edri icafnh ipfius bafis k1. b m riillu iiffgl . 10,". h ius. Imm a clams Cubi, adlmcm cadcm p 133.111- 6 €th i'cr ; 1.‘,, iLCcdemis. Per p1‘3n1i113.mitaqnlc,fx b‘figux tcxmmiruf 111 a h.Prlockulc1tur ail-zcomfpnulik LPCT 1 5"" {wins \'€191‘$m1fl1.1h 47km ., maior eius portio d E Scd pcr 29‘ . Indus, dimidio ipfius d {1.xquah's efl: (1:. At dg. per I;""..h11ius, cfl‘ dimidium. ipfius d'f. Ergo , pct mnucrfim , chtimx Rrxmifl} , ipfius d. adiuifx fecundfi‘m mcdiam, extra- t It, ' a b C. 8: ex b f. in fk. Produamr trmngulum‘ 1 . pct auipcmffgom " cx‘ rimam {cx{i,?cntag01111111 .1 b cad mangulum i& mquamfropor- 4] . Pl"In".(hllflr'xcdpi gm k f. Iqimr per 1 5"" quint pctfficxes (513:1; EFlI-‘u vidcllc In cm a‘b c‘fii pcnmg It)3 3:116}: ‘diltodclc-dplulfu 13pm . ‘ Iccr 1L1 totarp kl. b guh trian A ' I d v' racu~1um uplum hnex L E wgcc ad 11. a linem hun: decup P "BL a ' " "hm icofa‘ncdri: ficut duct d . f ‘ uom'am a h.efl: ‘ ~ ". a h.cfi ecu P lum x P ms 21 c. (‘1 Scd duodfluflum lPhdS dexmns we..." ._, > EVCLIDI'S (bier) fub Perpendicular-i5 centre bafis‘ dodecahed‘ri ad lam-5,135 {ub ipfor latere c0111prehend1rur, rcé‘mngujum» Fit touus fupcxficrcm dodccahsdricg pars tricefima. A centro‘buhs doacca- .u . Juan." 138 33 |