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Show 116 EVCLIDIS ELE‘MENTORVM cficularisxtrinqfic ad mqunlimtem ipfius k gnprominens. Conn :x'isci; ram 1. qufim m. punél‘o cum 4.":mgulis c fg h . complctum CR 0&3hedron quccfitum. & in (plan , cuius diamcrri 1m. 0 g. f h. &quam 'defcribit {emicirculus l e m. comprchcnfum. Ad cuius diamcu'um g1. 'ipib {phmrce dimctiens 1 m.potcntialitcr duplus eff. Cu'num conflrucrc, & dam fphxm comprehendere, CC gflendcrc IS qubd ipfius {thrzt dimetiens Fotcntil triplus eff ad latus iphus cubi. PROPO‘SITYONES. 117- Pcntagonum efg h k. & decagonum 1 m n o p . A quibus punc‘l‘is . excitcnmr pctpédicularcs ad Circhum l mu {in t.o up (1%? flnq‘ulx ' Iinta‘qualcs ipfi b d. A punc'fis aura-1'11 q 1' ft u. ling‘ulis dcducfl‘rur hypothcmifit Linm ad angulos Pcnmgonizqum fin: q k. (1 h.v h.v g. t g. t E {T {6. r at k.Ec quinquc alir rmnlhcrfit l‘ciliccc (1 r. 1- s. 5 t. t v.v q_ Conni‘flantVCrtiCCS harum pcrpcndiculnrium28c ficmm pcnmgonum Sit do. 9: {phacrzc dinmctros a b. ponaturque :1 c. 'duph ipfius Cb. flcut in pyramids. & ipfi b d. q r 5 t v.1‘quihttcrmn prima QB: cum latcribus vtrjnsq; Pmmgoni acicntdccsm tridngula rcquilntcm . Nam vmquccq(Linn-um hypo- themiihmm, pcr pcnultimnm primi,porcfi Psrpcndicuhl‘im, qucc cf! gquum fit c Hams Cubi :- Fg h1g1 m nfupcr 1mfim quadra mm 6 Pg hereai latcribus ad perpendiculd larus hexagoni ciICuli (g. &L1tus dcmgoni. & idco , par 155.11uius,c0: cxcitatis confirufli. Ipf}: enim in fphxm , cuius diam thra b.clauditur. Cum enim a. b.ipfius l? c. tripla litldco per 8".& 17‘ fextiqundmrum ipfius a b." trjplum cftadquafiramm ipfius b d. 8.: fimilitn‘ in : cubo fk.di;1mctcr,conneé't€ns oppofiros folidos angulos, qui demcticns efi fphmm: cubum circumferibéEis, , fotérialitcr triplumfiplhts c Harem cubiti Cui :cquaIisC mm b d. Igitur fk. mqualis ipfi a b. propofit-x fphxm', diann‘tro.Et perindc cubus ab ipfa propofita Sphaera circumfcribitur. quod faciendum 8: demonflrandum proponitur . ‘ . I . . . . D.fk{g_l}: FfD . FE. Igr potentla 1Pfius fk. (er continct porétii cu. 13;; . (biti latcris. Mani‘f‘cfium ePc igitur , qubd quadrata Iatcrum pyramidis & cubi .pariter {umpta , I ffirxquali: quadraw diamcrri r fphxm‘, in qua. dcfcribunt‘. Hoc . ____ a I c j 1' V cnim quadratfi vni {110mm (clbluialtcrfi per mite pm:- zqunlis lateri p6 ragoni . Itfm 5. Centre circuli e f' g.quod tlrhpun{hm} x.cxc1trtur ipfi‘circulo per . . pédicularis x y.qu;htipf1 bdquualis, ficut 1hr: prmclidx quinquc perpcndicuhrcs . Cuinppomrur in radium y zaqualis ipfi fn. inreri fcilicer dcca-L goni; & Cid rm Iqualis X z». Tamc'l; 2.. ~ V _ qudm (a . conncc'tgfur gun quipquc punch's pcnmgoni tuiticé'ci. Vidchcct z.cum pumftls q r s (v. At ver'o m,cum puné‘ds c {g h k. Vnde Hengquma V'tlimqughoc cf! dec‘em 111a ‘ triangula Prioribus asquilatcm. Qumquc ihlum COHCL‘L‘lfcn‘tla'ad z.. punéhlm : & toridcm ad w. puntlum. Vngquxquc cmm hnsarpm ‘ Porcrit hexagoni & dccngohi lams. 8111169 lmgulzr cum: requalcs lpfi c f. ipfx cnim m X. s y. fimt {emidiamctn'Clyculorum c fig. 3991‘s.zrqualium &_,lnrc1:a hexagonica corundgm: 11C Complem mm Vlgmu 5 5 ‘ trianguh icoflihcdrum comm claudcntm ._ . 7 .8: 8 peg c.1dco b lpfmn elk-ad b.qu1‘ncupla a ream. Er quoniam {cxti, quadmmm ipfius :1 b. quincuplum lelt ad qmdmtum lyfius b d. miiiam , reliquo uiplum CH: pct pm:- fed per 115.85 65.11m'us. (lunchatu‘m n) z. qulncuplum cfi ad qua‘dratum icntcm. Item patct qubd ac. altitudo Pymmiclis ad 1) d. latus vel altirudiné cubi potenzialitcr, eff ibilluitcrtia. ICOSAHEDRVM conflruerc (3: data. {phrera comprehendcre , Sc oficnderc , quéd ipfius icofahedri Iatus ipfius x y. qua: fuit (equalis iph b d 131g" :9 z. Equalls cit IP11 a b. & qxioniam- x- y. media Propomomhs clllmfer z y. 8c 2 x. Scildco mrcr iplhs z y.& y (a. Idcomm y squam X meh-X y.a:qu.1lls_1pcd1a proppxrtionniis critintcr portioncs diametri z w. , mrc {cmlgfculus dictFnptus fiipcr z (mdiamctrogbit pcripfa s 1n..pL'ICtJ.‘& {cnncuculgs ling: {um-r axe z m. {tame ibmel rcuolutus deicrfbcttphxram conrxpgcrcm irrationale tibxypclhiuré]; minor. Sitdatse fpha'rx diametros a b. 8: a c.qu:du'1plaflti1§‘)fiusb c.& excitam c d. perpendicularizduéhsci; ad d b.fia§ anfi ex Icmiciiamctro b d. circulus e Fg. intra qué claudatur .r . Penta- ' "1353"" "54329-41. - finAgqus icoffihsdriangulos. 3€P€tind€ ipllpn xgofnhxirum cn:cum{cribcntunfiu m (in: w 1411: iPh a. b.mqu;1is,mm iohdum lPium a data; H 5 {Phxu |
