OCR Text |
Show 1718; EVCILIDIS {Phil-1 comprehendetur. ELEMENTORVM p R‘ OPOSITI'ON‘ES‘?‘ Et quoniam rationalis efi b d.quando-v qiiidem in potentia commcnfurabifis ef‘r ipfi a b. per hypothefim \ rationaliddeo & m x.11h :rqualis mtionalis. cfr : fEmidiamerer fcilicc: Ump-VCImk-} EM 19 "whim. ., [La {a [I file m. m» e k.v:l a c. D circuli , cui pcntagonum 2 Pg. infcriptum efi . Ergo pcr14iliuius, & U- ' 5" " D .9. e. Ergo quadmt'im a p. quadrupium ad quadratum a e. & ideo~ a p. ipfum e Epen tagoni Iatus, quod cf: 8: icofhhedri Innis, irratiomlis eff, quac minor fofium ef'c g. quod faciendum , & oftcnfum quod often- Seccntur ipfm g h. k e. k f. fingulm fL-Cuudfim mcdinm extrem amquc . dupia eftil‘vflus a e . Et pcrinde :eqns-lis fare" cubi a d . Simihter of‘tendcmus: quéd d n. a qualis Lf‘: Ciddn a d . Qua-clam- 3i ptimi, tam anguius :1. n pgulm angu'us n p quuaiis eff nngulo a r d.Eft('1uc pcntsgcnum:eqni'aterum : ficutdudum Fuit dcnionftratum. Igitur per 9‘.huius,pcnmgcnum a n p d iaxquianguium cf‘t.Non aliterfiipcr Vnumquodq; reiiquorum vndecim laterum cub! compareturpentagonueraquc duodecim ptntngona ccmfonentdodecahedrum. E: rationcmdn punélis ql1n.funt¢'1uemaiomfegmenm g (1. k 1. km. nwulis ‘1 uibusfi , a ‘‘C (I ualcs lint fing nix P er P endiculares r. [‘1 uiiem ad L planum a c.ipfa: nutcm ln.m pad planum a b. Connex‘1isquc punftis , a n P d r.fictpentagonum mquilaterum & :cquianguium (kl-6d cnim Lit mquilatcrum, fic Pater, cubus . (ltzod fic demcnfh'atur. Duo plana per ru'hs h k. cf: fecent cubum: quorum pinnorum communis f'cétio fit ipfa reéta o k. qua: fecabitur 21 diametro dcndum proponitur. DODECAH w RVM confh'uere , & data f‘phxra comprehenderc : 8c ofh‘ndere q; dodecahedri lAELES fl‘l‘dthnulC cf}, & appellatur npotome. f1 rationalis fuerit {phrase diametros . Duarum bafium cubi conti- giinrum a [m clarem duo": d.& d [3. Cum Oppofito fuccntur fingula , PCI‘ xqualin in pu'néfis h f‘e.du<§‘tiso'l; c fig 11. h k.pcr centm bafiumigk. i DJ‘: 2. . y4hul' circumfcribitur ab eadcm fphmm , :‘z qua 8c cubi. & fecabat viciflim mm per :equalia. D in centto cubi,per 4O.Vndec1mi.Sirimquc .centrum cubi. & fic argumenmre. In DahgvclaLaé - gflgklwelln. [3.3. n. I]. e L . I] 1:]..1 n. "(3.111. Ergo :1 Ldupla ipfius k L quare xquaiis ipfi lm. & idco 1'pr n p. Et fimiliter OitCDCiCanS,qll(\)d d p.ipfi n p. quodque a r.r d. linguist fun: ipfis primis lines: o 3.0 d.xqunles :grioniam femidiamctri funt tam cubi, qhém {Fluent Ber 40"". vn(.cc1mi & 18"". huius.& (1:13 o kipfi ek.& a n. d p. fmgulis xq ualcs. ' k s.ipf1 k m. funtmqunles :Ideo 0 s. in Punéto k. fecarur extremch nap. t _Q\Ll_9d:1l1tcln totum pentagonum a r d P n. fit in vnoplano, Sic pater. Exeatk s. ipfisl n.k p. parallelus : 85 idco cifdem :cquafis. 8: plane a b. perpendicularis . Eritci uc ficut r (1. adfi ‘ ipfam q hzfic h k.ad ipfam k s. Nam in iinea feéta extre ratione,fic cft rota ad mains, ficut maius ad minus fegm ma & media cmum. Ergo. triangula r q 11.11 k sfunt fimilia: 8c quia funt in vno piano, 85 latent r (1.11 k.Itcm ipfh q h.k s. funt aequidiftantia : ideo per 30é féxti, Iin :2. r h s.cft Vim tech. (Quite per 1" vndecimi r h s. 86 a h 61. rear: fun: in V110 Plano : & pentagonum ipfumin vno plano . 116d veré fir mquinnfrulum, fir; conftat. Cum 6 k.. fit feéh in punékor L. ecundfim medi um xpia quoquc 6 min punc'tok. fimilitcr feé‘m cf}; Vnde fic argue r, . . ~ . mut~ _- ...~. .1", firm...» » (54 mains feomcntum D i ' i C]. o s. _--- a "gagkme [:1 Ergo quadratum ipfius o p. tripium eff ad quadratum ipfius :1 c. Sed a e. dimidium eff lateris cubi. Igitur per 18. poteflatem o d. femi} diameter eff fphmrx. E: fimiliter oftendemus , quéd Si punélo owe-6k: vniuerfae ad rcliqnos angulos dodecahedti funt femidiqmetri fphxrx: cubum circumfcribenris. Cumélue S.ex angulis 8 dodecahedri fintfimul cfi angulis cubi, ficutqui adipfaa d. punétazpater quibd fphmm ipfa, (111.1" cubum,circfifcribet dodecahcdrfi. %od tandé latus ipfum dodecahcdri fit apotomigfic pater. & extremam rationem : & kmfitxqualis k Lmalori fegme nto : ideo Per yihuius, c media rationc. Vnde fic procedc. [1p s.velsk. r h . (My. Agatur r p. qux fecnbir iprzm a d. fecundl‘im extremam &1ncdian1 rationé per 10"". hnius. &' a K c mains fegmentum eritipfi a r. requale: cumt'luc idfit potentia rationalis ( quoniamfyhxrm diameter m rionafis) idea H 4 a r.iatus |