34S Encydop^dte Lib. XV. 



£t hie ^uidem ejf eonus reHus ; ^HemfolHm Euclides 

 ^^ngmt. De ohU(]He vide in rejrults. 



Cylindrus eft, qui i fupcrficie cylindracca & op- 

 pofitis bafibascomprehenditiir. Et coufiitHiturcon- 

 uerfionefarAllelogratrtmre^anguU.altero latere ^ttief- 

 ttnte : vteji J^O P. 



Cotpus*vt ' 

 Mocieetui} 



Corpus 

 «uomodo 

 diflingiu- 

 luti 



Ger.emli» 

 ptincijiia 

 flereome- 

 Uic. 



quantui ei fimilitudine planorum fimilium , &: «rura prapor- 

 tionalia funt ipf^ Uipe(ficies,& ideo propoitionales,& fimilcs. 

 5 . SoUdafimilia, hahent trifltcntmi, rationem horrtologorum late- 

 rum , O- duo mediaproporttonalia. Vt funto 4, cubi hoc modo 

 CubM, Longttudo. Latitudo Ahitudo. 



I. 5. i- 3- 



II. 5- i' 4. 



III. 6. 4. 5- 



IV. 10. ■ 4. 6- 

 Dico primum complciSlilibras 50, fccundum «Ic.tcrtium iro, 

 quartum 140.6...^«^«/« flani cortiprehendenti-sflrigulumfolidum 

 funtminores quatuorrciii!, Nam fiquatuor icflis Kijuarentur, 

 complercnt locum planum,net]ue omnino angulum faccrentj 

 multoque miniis.fi maiores forent. 7. Angulus reiius folidm 

 comprchenditnr -vel atribusplanis rcftis trianguli ordinati,.vt 

 in tetrovdro : vel aquatuor, vt in ociaedro: vel aquinque,vt ia 

 icofaedro : vel atiibus quadtatis angulis, vtin«(i'5 : vcl deni- 

 quc atribus angulis quinquaflguli ordinati,vt in dodecaidro. 



t V. Diameter cerporis dicitur axis : & termm a.vis Axes 

 dicumur poli. ^*'''' 



Axis igitur eft , circa quemiconuertitur corpus:vt a e : poli 

 Et hic quidem efl cylindrus rcUus. De ehUquovide funt punda axem tcrminantiatvt 4 &«. E.i5.ij.ii.d.ii. 



t regHlii. 



R E G V 1 i€- 



/. CorpHs creamr motufnpe^ficieifnhjtdentis 

 gfr^ crajjefcemis;,. 



Qnemadmodum linea: terminus, fiue extremum, tuit pun- 

 aum, & (upcrficiei Iinea:fic tetmiims corpons eft fupcifacies. 

 E. i.d. I i.Sicutergaex fluxu pundi in longitudinem,lJnea & e 

 motuline.^ in latitHdweni fupcrficies : ita e motu tuperfaciei 

 in alt!tudincmfiueptofunditatcra,ade6(jne in crairmcm.crca- 

 tur coipas. Vndedicitur altitudo,profunditai, crajpties; '&• trtna 

 dimenfio. Eiu^ Geomettia dicitut Srtrwmtn^ , qua^fanead- 

 modum e^ccUit in vniuersa Gcometiia. Ea quippe docet ra- 

 tionem menfurandi corpora : c' gr. capacitatem vafis. Ylato 7. 

 de r«f ." conlquciitur , hanc fci.cntiaiTi (iteieometriam) nondum 

 i/fuentam : ide6qiie.'ec'nfet publkis honoribus &p.txm\is cx- 

 «Jeilentia ingenia ekcitanda adtantx rc^ indagin£m. Itaquc 

 l^latonis velut authoiiitate perraoti Aichimedcs, Thcodofms, 

 . Jfi.polionius, Serenns ,' Pappus , & alij , jA vacaas pofledionis 

 huius paites-Liigifffi mirabiles fhuajjrts.fecere. Alioqui ftc- 

 leoipctria in erehicntis eftiexigua- 



'IJL. Cdypw re£ie dijiinghitHr ex Jufrierminis. 



Queraadniodtim diftlnaio fuperficietuaii i; fqis , fcrmmis 

 eft aflum w.ita vt fupcrFicics a linefs rcctis denominewt.rea^- , , 

 linea.ab obliqois obiiquilinea : fic, difFcrcotiacorporum afuis • 

 itidem tcrmmis cft.Hinc^corpu'k diiiidiiuj: prima CSJgeneralif- 

 fima diuifione in planum- &' gtbbum. Corpus flaniam cft, 

 quott^omprelienditur-aiiiperficiebusplanis. DiftinguitutauT.- 

 tem planum corpus a numero p!anoru9i,qua:.Ue«/ (^" ' '^"'^F, J 

 tetrahcdrum, pentahodruro &c vel omifia afplratione.tettae- 

 drum, pcntacdrum &c.POTfo^U»MCtiilineidilfctentia: fue- 

 runt anumero lateruinve^«(»^ulSuiiM.i'Wde trilatcrum,qua- 

 drihterum , muItilatcriUa»^^./ trtenauljJjnN. quadiangulum, 

 mulfangulum. Sic codtoris pfani :3ift«rentiJ funt a numeto 

 tetminorum, quos hcd|ardiTJH>»s{ appel-hfTlSed alitcr quam 

 inplaiiisfcrjcs perpetuV-efti^Jpyraniidei.qaaternatio^in py- 

 rainidito autem a qmiuVio. Nun^cn^ an^iliorum numcio 



terminorum fiuc hedtaT'uKnan';pCjrE?^-*<='l'°"''^^' Py^sr"'^ 

 tetracdia,pentacdra,polyedrai-«ft;4ilidetTi quadrangula. quiii- 

 quaii!;iila, mulrangula ; fcd prifraa pentaedrum eft fcxangu- 

 lum_,KeXacdiUm, o.^Jtajigtfittm.&ita deiiiceps,';; .U' < . ■ • 



/ / /; Generalia [lereometrli: prtnctpia H^cfmt. '. ' 



\.Vi linea per. imtM, fuptrjiciesfer ftipt'*fioHifitiv lOrpor» ptr 

 eorpufcuiaMcifJur^itHti Rits eniija Corpotis quxlilict corpiis i, 

 eft.Hic ii^aftua fnenfuMCoaditiones.lliu; r^-_^iiifiu,cnam loc jm . 

 liabent. l.Ui^bii^iJia ^uTnmfolidumniJireciutn fufciftt, Soli- 

 dum vcro reftum cft.cuius aiis ert peiwendicularis ccntro ba- 

 fis:obliquum contta. 5. Si foUda fAiprehenduniur » fnperficte- 

 bus homogencif Aqualibit.s multttuaitti .O" magnitudine, ftint s.- 

 ^fWia.Vt duo cubilunt afquales,quoruni lcnxfuperficiespla- 

 na;funt a.'qua'ies:du.T fphasra: funt a!quale^,quarum fupcrficics 

 fuHtsqua'cs;duo coni,cylindi:^que (uiit'.^-quales,quoiufuper- 

 ficies fupeificicbus. bafes ba(i)!>Us faht £qualcs. Neque tamcn 

 Jiiilc dixcrls ifoperimetra foijda quilibet effe rqualia. Fallcre 

 enim poffit in hcterogenci^^. Si foitda comprehenduntur a '«- 

 ferficiehus multitndine ^/idtihuf ^ fimllibtii ,fH»t finitita.Fi^a- 



see enira fimilcs funt xqiuangulK ic ptopdrtionalcs cruribus 



z^Oalium angulotum.At in folidis planis fimilibus anguli x- 



Et itaquidera axisaccipiturlate.Stridetribuitur folifpha:- 

 tue.Porro angulus corporis eft folidus : cuiufmodianguli funt 

 in cubo feu tefTera. 



y. Pjramis ef omniumfoUdorHm prima. '^y 



Quemadmodum triangulum eft fimpliciftima fuperflcies: 

 ita pyramis eft fimplicifllmum corpus ; & proinde prima figu- 

 ra folidarum. Quemadmodum igicur plana orania in trian- 

 gulji;.fic omnia folida in pyramidcs tefoluuntur, quac idcirco 

 appellantur/i^ra^niito.i, ficuti (uperficies c triangulis compo- 

 fita; dicuntur triangulata. , 



VI. In vmnersa rerum natura nonnif ^iiinque corpora '^' 

 ordinataplana reperiuntnr : videl.tetre^drmn,cuhn6, din: 

 e£laedrum,dodecacdfHml^^co/aedrHm: & vnicum 

 dunta.vatgihh^m,-Z'^eifphitra. 



Corpus regularejfiue ordipatuin, dicitur, quod bafes,Iatera 

 (qua; hic dicuntur hcdra:)& angufo^ afquales fimilefquc habet. 

 Hoc nonnuHi fubdmidunt in firaplex & cpmpolitum. Sim- 

 plcx , ipfis cft fplia:ra , qii* conftat fupcrfitie vnius generis, 

 Conipofica,fiue mixta,funt, qur ctfi baiiiicircularem habeant, 

 varia tamcn planitip conltanr. Ec hic illisffubdiuiduntur in 

 principalia& minttf 'prillripirHl.-flla funt qdinquc pauloante 

 difta.Corpora fiueToiida regulariaminus principaliafuut co- 

 nus&.,c^lindrus.Irtegiviaii^'^(jorppra,illisip(ishqiunctij:,qao- 

 ruSl\yii ita dcfi5it<i;-tunt'"re2;u& ,' nec vfus in fvUthcmaticis 

 ad8"^"^W»qnenratus .&■ rt^JtfeiT^^iusH-t ■funT'c'o'rporh''lcnticulatia, 

 oualia,&c. Vcrum hxe inpthodus n6n cft farts accHtate' Nara 

 fpha:ta non eft prima figura folidatum, fcd pyramis. E: quin- 

 quc duntaxat funt corpora plana propriillimc ortlinata, fiue 

 regularia :quia omniaplana, quibu.silla corpoia conriiientur, 

 funtafqualia : quippe a;quiJaEm-6e: a^quiuiiJula. Dicuntur cor- 

 poraPlatonica : Quia Klap in Ti«ia'o, qninouc illa liinplicia 

 mundi corpora, ncmpc coeluin, igncm, acrcm, aauam, & ter- 

 ram , quinque iftis cor[vtibus aflimilauit. Pyt!irfe;cias autem 

 theologiam quandam cx ifHs corpc/iKus lepcrit ■ tanquam 

 mens illa funiiiii Dci fapientiaque dc falrican40jn.i;iuid'>,& 

 ordt|iat)%''corpori^usJ^Wrnando cogic^ns ftcreomctrix liu- 

 iu^rdf^i,hbiptoperucric. Quo pertinct ccIcbre"iUudPlato- 

 nis,*£«» ut]j*ufti7tii. Ca-teroqui Clauitts fuh finc?n ip ttulid. 

 dotSiflimc demonftrat , pta;tcr li.Tcquinque corpota icgula- 

 ria non pofTc aliuddari regu'ia;ejidclt,tale, quod conftetpla- 

 nis inter fea;quaIilius,idcft',£EquiIateris & a-qulaiigiili.^^.Exan- 

 guli folidi naturii pctfpccics planarumfigurarumhoc itacon-- 

 ficitur. Aduobusplanis angulis non comprehfiditut folidus 

 anguius. Ex tribus angulis trianguli ordinatj cft angulus tc - 

 tracdii i cx quatuor,oftacdri ; ex quinque.icofaedfri ; e fcx nnn 

 potcft ; nam fex plani talcs anguli valcvcnt li^tcttias re;>i, 

 id cft.qu.nuor rcdos. At anguli plani facicrftcs foliduuiUuiL 

 minorcs quatuot reiT:is. E fcptcro igitur & pluiibus itiulto 

 miims cft pollibilc. Equadratis tribui anguli.s conipicncii- 

 ditur angulus cubi • c «luatuor non jioteft ob eaiidcni i::iu(ani. 

 Etribu.< angulis quinqujn:»uli ordinati elt augulus dodccac- 

 dri". cquatuornon potcft.nam iinguli valent ttctmn,& vimiii 



quintam 



