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Show 132 EVCLIDTS SkoposxTIONss. ELEMENTORVM P;;c;niff},crir fuus icofhhcdri dcfcripti in fphxm , cuius f'emidiamc-rcr a b. thuoniml a 11. qu.:drupf;1 thpfius h b. ldco qmdratum ipffus- a cguxdruplum crir‘quadmti b c.& a c.dup1:1ipfms b c.& b d.mqmlis igfi a b.1111), per 11" . fccundi, quod fir C); a C. i." ipfiun c bgtquum cfl‘ qmdmto ipuus c d. atqu: idco Per 1 6". fcxti. fr 3. c. fcccturfccnndum cxu‘cmun &m:di'1m 1111;100:111311‘1 lior cius portio crit c d. Vcl quonilm :1 1». ad ipflun b c. porcutinfircrquincupfa eff: idco a C. (quce duph cffipfius‘ b C.) diuifn fccundum cxrremrm 8(1112‘diammtionem, mirror: cius porrio Grit C d. per 2."" prrmim lrbri . Producatur c a. 8: pomrur c f. 1:1tuS culvi in di€t1 f'phmra locati. Q3_od quidcm ad femi‘ drum-mun potsntiufircr fchuircrrium eff. ad ipfam vcro .1 c. ficut 5. ad 3.& agmtur C Efgipfis d (1.5L bmquidifhntcs.Vnde CX fimilirudinctrimgulorum fcqucturproportio finmrum. Atqucper 7‘m ptccmiffi, ficur ipfius a cfccundr‘un extrcmam <3: median} rationem (iiuifg maior Portia eff: C d. in 85 ipfius Cf. fimilitcr {ca; maior pars crit. cc. Cum-31116 c f. fit lltllS cu'aiuum Per 2.0"" Prrmiffi , c c. fiet latus dodccahedri in cadcm {plum claufi . Si aurcm pomtur a c. fcmidinmstcr circuli vcl latus hexagonl:Tungquoniam a c. Pcr medium 8:: cxrrcmun rationém {65hr mcuor portio cf]: c d. [dso per x 2. "‘ r33 quze componiturex b c. diéb dimidio,& ex c d. Iatere decagoni. E; hoc eff: tcrtium corollarium . Nomndum criam qubd 117cc cadcm corollaria fequeba11t11r in dc. fcriptione6clinenmmto 19. prmtendcnris libri. Si fphmm circumfcribat dodecahcd rum 6c Cubum: runc Iatus Cubi cfl: linca,quac fubtcndit angulum in pentagono dodccahedri. Er hoc etiam corollarim confiat in 2.03 prmmiffi. Nunc veniamus ad praxim Calculi theoriam comprobantes : 8: {phreraz femidiamcrrum partium 6. ficurantca, ponentcs. A bfcmidiameter fphzrr; c f. latus cubi 1:48 a h. c . m 2. h b. c c.1arus dodecahcdrixfiofi Lu. 6 11 qu finguln refpondcnt ac iis , quze fupcrius de. bc monfh‘antur. a d. Iatus icofhhcdri. {cilicet r. 72.. Ex. [.103 6 § , Hafienm qua: circa [atom @v [24ch ac perpendicular‘e: pyramZdir, ' ofiabcdri , argue cubi (9* comm collation". ncc non circa latcm ico zzbedrz' atque dodccabedn‘ corgfira'erfmdafimt, tradidimm . Dez'nceps adpcrpcndz'cularcs, (mfg, flcperficic‘: acfolidi- cares bomm duomm , (r collationem demon/fran- prmniffi c d. erit 1:1tus ducagoni 31 mli dam mm'cmm. 24;" binc fccmzdum bunc libcllum termimlzimm . circulo circumfcripti.& Per 15"" a d.latus :3 pcnragom. Er quoniam :1 C. ad ipfam a b. filmi- A C a N 'r R o f'phrerre ad bnfim icofahedri rec'la perpendicu- z; diamctrum fphrerx porcntiafiter cffficut4. ad 5. Etipfius a C. (H610 Iaris maior cfl,quim pcrpcndicufnris ab eodem cétro ad bafim mod.) diuifcg maior portio eff c d.1dcofcquitur hoc corollarium,quc‘>d ipfum a ddntus icofahcdri potefl ipfas a c. c d. Item) quoniam a b. fcmidiamcter fphmrx potentialiter quincupfa cf]: ad ipfam b c. quod eff: dimidium ipfius a. c. ideo diameter {phxrzz potentixlitcr ctium quincupla cfl :Ld rotam a c. qux eff: femidiametcr circuli circumfcribcntis pcnmgonum , Cuius Iatus eff ipfum :1 d. latus ico ahcdri in talifphrra locari. @961 autcm Iinca a d. fit latus penta- goni in diéio circulo pofiti, pater per 135 . pmemiffi : quoniaufpotcfl cubi in cadcm fphxra con f‘riruti. Pacer. Nam CerlIflls circumfcribc's quadratum Cubi,maior sf'c Circuio circumferibcnrc trinngulu m icofahcdri . Nam iffc Circufus , per x1.j huius, CirCrunfhrth triangulum oc'tnhcdri . quod triangufum mnius CH: trinngufo icofnhedri, quad circumfcribir hic. Ergo fi quadrnta horum f‘c midinmctroru m fingufa fubtrnhzm ru r 51 quadra to fhnidiumctri {phi-rm; fupcrcrunt pcr penul- i p111 a c.c d‘latc-ra hexagoui 8: dccaqoni :‘1 rali circa-Io Claufulomm. Et habcs fecundfim hoc'corollarmm: gonffar etiam quéd fphxra: femidiameter :rqualis CR dimidio late-- timnm primi , quadram pcrpcndicularium ix ccntro f‘phmrm ad ‘1)th folidorum bafes‘Pcr firbtruéfioncm igitur minor-is qundra ti, fupcrcrit muius quadrarum, & idco major pvrpcndicuhris . Quninm igitur minor c‘fl‘ Circufus Circumfbribcns bnfim icofuhcdri , 8: idco minus quadratum cius fcmidinmctergidco maior crir pcrpcndicularis £1 cérro {is hexagoni & latcri dccagoni in circufo prrdié'to dcfcriptorfx packer. {phatrx ad bafim icofuhcdri , quém ab codcm cenrro perpendicularrs acceptis. ad bafxm cubi. %od cf} propofitum. Namqu¢ a b. fphxra: fcmidiametcr xqualis fuit ipfi b d.‘ Potcmt & prius oflcndi,quud' I ‘ quz 3 perpen- |