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Show 4o~ · . . eAppararu"'J · Pappus propofidone ro. Jib. 8 • .Erycemi Paradoxa, :Eratotlhenis Me fora; bia,cuius fr2grneowm exeat in commene. Eutocij in Archimedem. Dtme4 t rius Ale~ 1ndrinus de Jioearibus aggreffion·ibu:s pag. 6t.Philo Tianams e~ imp!icactone 7rAnx,1o~I'-Jv, pag. 61. Hi ex Pappo. Tandem D.emocr.itus, & Anaxagoras, vt refert Vitruuius Jib.7. de e.ad.em refcripfer.unt, quem~ admodum oporteat ad adem oculorum , radiorum extenfionem certo to~ c:o, centro confiicu.to,,ad lineas r.atione n4tura.Ji refpondcre, vci de incerta re certz imagines re~iiiciorum in fcenarum piauris rcdder.enc fpeciem,& qu~ in dirccho planifque froncibus fint figura ta:, alia abfcedentia, aliL prominentia elfe videantur:horum dochinam,videtur innoualfe Marchio Guidus vbaJdus in fua Perfped:iua. Federicus etiam Comandinus pucat vecer c s de ceo cro gra uita tis foiidorum fcr:i pfiffe , cum Archimedes de infidtntibus aqu~ centri grauitatis Coooidis fecerit mention em. quam par~ .tern ipfe c.onatus eft renouare , fed earn Lucas Valerius multo magis am• pliauit.H~c funt ig.itur diuina ilia veteru monumenta,qu~ ob fuperiorum· fc:culorum barll:uiem inrercidiffedolemus: qua: forte ~pud Arabes , auo ~lias nationes fub alio idiomate lacicant , donee Princ:ipum noftrorunw 1udullria ea requifierir:. ,D' G eometri~promotitJ11t, ex arte geometrice demonflrandi, rvbj de l(fjolutione. H Oc1ocd mei-~~neris ~lfe animaduerti non nulla ae arte Geometric.e . dcmonllrand1 m rnedmm afferre;quandoquidem ea eft quz ca:tens ommbu~ matl1e?l. ~p.irirum.ac vitam quodammodo infundu:, & qua reliqu~ ddbtuca: (ct e~1 tJ ~, a_c philo_fophi~ nomine prorfus indjgn-r videantur:· pr:rterea qu,o mre qutfpum tlbt machematici nomen arrogare audeat,qul nee fu~ .rc_&e demonflrare, ntc de alien is rea:e iudicarequeat. hac veteres ~agn~. Jl!I Geom~tra: f~ff11lti mirabiles ill as demooftrationes, quz noflris mgenJJS tmpoffibtles VJ d~n mr, felicicer excogitarunr. Vcinam aucem ex~ ta-:fnt ea quz de ea Euchdes, A pollonios, & Arilta:us c:onfcripferunt; non c~tm opus nunc elfet nos in ea vrcunque adumbranda Jaborare. ~am· UJS autc:.m.hanc .arcem ,vt bene air Petrus Noonius cap. 4· de err. Orontij,· ex 9uortdaano IIbrorum Euclidis & aJiorum Geometrar~m fiudio & imi· r~rwne con!equi po.ffimu,, facilius camen addicis fcquc:ncibus annotario• rubu~, eam confequemur . c~·id (it Geometric a demonflratio.· D Emon~.rjtioGeo~ecrica e lt difcurfus cercus, & euideosex veris, ~ propn}s Geometn~ princip.ijs per Enthymemata ad conclufionem ' procedens, \ -.J Ma1~tmatl(tii, ':4o1 ...... proceden·e. Yt autem·beneinteJiigatur quid fifv.eritarcoctuRcnls Gtomot ·tnc,r,& alia hue fpectantia, kge tract;. rum nofirum de natura Mat~ema .. ticarum in fine operis' notlri de lot is Mathern. vbi di"c~tum eft quid !it M~ ~ crria intelligibilis , qu~ fola capax eft geometric~ Yericaci;s, & perfc:., Clionis: ea au.tem eft quantit s abftra~a,&c.tlc vera & geometric:a ~qua,. Jitas ea eft, qua du:rJv.g.linc:t ira hmt ~qualcs.vt oullum omnino difcrimeh in.terlit 1 pon foJum fen.fibile , fed ne~ intelJigib!le. qu•idam cnim ad {er1fum videri po[uot 1tquatia , quz r:~m·en .. ge~metdce & vere non funt z~ qualia, vbi notandum ell 'Geometram,dum demonflrat, fupponere fe ha• bere kane Mlteri3·m intelligibilem. pr~fentcmiatque in ipfa pofic fe operari ,, :ideft, ducere in ea linea£, aogu1os '· tdangu la , &c. & quanui~ in fue Abaco delincet Jineas & fig~ ~ s fenfibiles ,·non tam en propterea ( vt aic. Arifi.tex. IJ. primi pofl:er. )fa lfi m rupponit. quia delineatiooes illas fenfibiles pro intelljgibitibus fuppo nic, vc meljus intelligacur.& vt ait Arifto• tclcs Geometra n.ihil conclud1t c~ quo,rl h~c; eft Hoe a fea6bilis, qu;~m ipfc cxponit ,.fed virtute illius intelligibiJfs' qu:r per feofibilem o~eoditur. " 'luanuis hzc materia inteJiigibilis nulla nunc cxtarct • fati$ eft fi pofiic c&--· urr, fdcotia Coioa ablt:rahic ab cxiftcntia fui fubictti. l -4 FM•A Geometric4 Demonflrationis. ' I H.Anedebtmuse1icereex Euclidis,& ~liorumdemonftrationibus quf Primo loco ponit Propofitionem, quz fcilicet proponitur vt probccur, vel vt cffieiatur; illud dieitur Theorem a, hoc Problem~ . SecundG Propofitionem explicat appolira figura, quz in problemate c:ontinet qua:. dam Data, dantur enim vel pund:a, vel line~, vel anguli, &t. fie in prim~ Euclidis,dacur linea vna, in fec:unda datur linea & pund:um.in Theoremate: exhibetur tigura de qua paffio demonftranda cfl, ideft, qu~ eft !ubiedi demonftracionis: fie:: in quarca exhibentur duo triangula , de quibus ctcenonll: rand~ fuot ali quat ~qualitates, & in ijsexplicatur propofirio. Tertio, ft~uicur Conttn .. aio, vt p lurimum cnim przter data., & fubie¢liL'1..t J~Ucffe eft ad demooltrandu cofhoerc alias lineas, fel aogulos, vel circ;u .. los,&c. fie io Prima Euelidis contlruuotur duo circuli, & duz Iineef. i~ omni problemate occelfaria eft confh utlio faltcm i t>fius problcmatis. ju__ Theoremate, nulla ~Jiquando opus eft tonftrudione, vc patec in 15. primi. ~arto; fcq.uitur difcurfus tirca Jiguram confirudam, qui proprie eft ip· fa De oftr.atio proceden.s per emhymemaca,qu2r probat aut fa&1:1m cae. aut vcrum efte ., .quod proJ>ODfb.3tur .. hi autem difcurfus gcometriei de· b~nt dfe brcue$, & limplu:cs, & pr.opttrc:l nihil in ·cis reperiruf, quod ex przcedentibus non fit iam manifefium,,6l ideo pr.oc(dit enthymematic~ non fyllogi~ice; qua~uis P?ait .ad f~r~am ry1JogiHicam reduci, ~r pa· 'ic 1a fchob~ f~ Cl~UJJ ad pnmam pnmJ 1 ~~ j~ diet JonBu~ F ~ tzd1:: rsa |