Geometri^ Pars I. Cap. IV. 505 



•.tU- 

 c!-. 



XVll- Llnea perpendlcnUrii,fiu nermalis, » Kcc.9ilQ-, 

 ejf mater CT magijira Geometris. & yirchite^onicd. 



Tantus nimtrum ipfius cft vfus in duabus hifcc difciplinis, 

 v: illa: fine pcrpcndiculo non poflint conliftcie. Ell autcm 

 duplex perpendiculi vfus. I. In exploranda linea redaerccla, 

 puta in muio.i. In explcf.inda iinca rcfta iaccnte fiue plani- 

 tie.Nam ciim filum exaflc incidi: in perpcndiculi balin.indi- 

 cjtiir longitudo librata.Hic obfcrua,quid Ct linca furgms. Sic 

 nconpcdicitur linea.qux' furgitcplano.pcripherii.vcl hclicc. 

 Reci» fnrgens e plano efl: , qus ab cius ccrto punifto tolli:ur. 

 Atquc etiam refta furgcns dicitur , cum aduenit abcxterno 

 puncflo , inque plano tanquamdelapfa fagitta figltur. Huius 

 vcto doftrinx pro ciemplis cxcroploiuui funt vmbtx : cum 

 furgentium vcritatem fola pcr fc plaDitics non capiar. Ergo 

 normnlis flano recia cft , qua: vndiquaquc arqiialitci partibus 

 interiacet, quomodo columna recfta ftatuitur, quomodo aibor 

 aut cauiis re£>us e tctransifcituneWJ^^/icontta. 



XVIII. LineiC perpendicnltfris tnjlrimentum efi 

 nortDa & petpcndiculi.m. 



Primum inftrumentum Geometricum in lincis tclis diti- 

 genidis tdregulx. Secundum eft circtnus , in difcribcndacir- 

 curafercntia. Tertium eft «ofOTa, j*aif<a?v, in linca rciLta rcdte 

 etigcndi in codcm plano fupcrrcifla.atque inde in fuperficie 

 ic corporc fnpcr fuperficiem cotpiifue.Quartumcft/cr^c»;/!- 

 «/««•.jwf^it.einticbtfcbiiut/cinfeiuFcffchmir/q.pcrpendicu- 

 lilinea. ^Clicfcf cft perpendiculum , a fencFcivmergerCjde- 

 mitterejvti Grarcis i)>t««»T(!^',«aS-<f»af ell fubmittcrc,dcorfum 

 llbratc, vnde &/itr<i,ac /ifefilU, dicicur. Ha;c inflrumcnta qui 

 litc poteft adhtbcrc , plurima probleraata intclliget , quar ab 

 Euclide admodum moiosc & opero.sc demonfttantur. Ca:te- 

 tum pcrpendiculum conftat cxfilo ^ plurabo, ij: arcliiteiSis 

 dicitur feiicfcl/ itcm fjfcowag & fclci)3C*ticf)t / itcm Bas' 

 fcl)rOtgcwicl>t/ & pcrcxcellcnriambv^B blco. Quod quidem 

 inftrumentum ci hoc ptincipio phyfico cxtruiflum cll : Cor- 

 tu4 grauefertttr deorfumlinea breuijfimd. lam vcro pUunbum 

 fccundiim aurum eft corpus gtauiflimum , Sc linea rcda cft 

 brcuilfuna.Talis eft linca a t. 



It Iioequidemeft perpendiculumphyficumtgeomctricum 

 oportct tnentc concipcie. 



XIX. LineA eidem alteri paralleU, interfe quo- 

 ^ue fmt paralleld. E.jo. p.l. 



Demonftratio petitur cx illo axiomate : ^lus, -vm ^eidem 

 fitnt iqualia.interfe quoquefimt iqualia.hem ex ilIo:Si £quA- 

 libm addantur tquMia, totafunt iqiiitlia. 



XX. Littea perptndicularis excitandit efl vel e punSfo 

 in datk re&a,vel e punSlo extra datam. 



Pcrpendiculatis e punfto in data refti excitanda eft vcl c 

 punfto medio, vcl alio quocunquc. E puniio medio eodem 

 modo excttatur,quoreda bifccaturffr rc^w/A;» <»«i«j cap.no- 

 Ham. E punclo non mcdio in linca data cxcitatur pcrpcndicu- 

 ]aris,fi cx punflo daio dcfcrihatur periphcria,&; ^circg.rionam 

 huius CiJ/i.crigatur perpendicularis. E. g. Sit daia rcfta a b, cx 

 cuius punclo d (it crigcnda pcrpendicularis. Primo cx d dc- 

 fcribatXjr circumfcrcntia. Dcindc portio lincse e'e diuidatut in 

 duas pattes atquales/tr regiilamdiciarp.Liazid fcxkpecpen- 

 diculatis. 



E pUKcio extra datam rciTbam ducitur perpendicularis, C ex 

 pun(flo dato defcribatur periphcria Uncam datam vtrimque 

 fccans. Tum eniiii portio linea: intra pcripheriam petrc^.wff- 

 n.im huius cij/.bifcdla cxhibct perpcndiculatcm : vt linca data 

 rcdla f\t a b,Sc punftum cxtra illam fit c; e quo perpcndicu- 

 laris fit crigcnda.Ponatur crgo pcs circini inpunctof.Sc du- 

 catur circulus a k g, Tuni linca df birccetut cx reg. 9, huius 

 cap.&: pcrpcndiculariserit^ h. 



Ex his patct lineam perpendxularem efTc breuiflimam. 



XXI. Linet. inter fi cellatx , funt homogene&y 

 vel heterogened, 



HomogcnetL, funt eiufdcm dcnominationis : vt parallelx & 

 ^aiallcLc , petpendicularcs & perpcndiculare.";. Heterogenea, 

 funt diucrfa: noracnclatura; , vt j>arallcla;& perpcndicularcs. 

 Ita perpendicalaris6c inclinanslunt hetcrogencas. Indinans 

 aiJtcm cll,qua: ina;qualiter interiacet: vt < 0. 



linex 'ho* 

 mo.Kenex 

 & heieio- 

 genc«. 



yl 



XXII. SiparalleU cnnterrninent pHralleloi, oppo- 

 fit£ £<juahumHr. £.34.^.1. 



Vt ab Sced : itcm ac Scb d funt iqualcs : quippe oppo- 

 fita-,& ipatallelis tcrminataf. 



a b 



XXIII. Si line& reEl^ parallelis pluribHs interficentur 

 figmenta eritnt proportionalia. 



Vt ficut /t & ad a^.fic acaia rf.Et inuersc ficut ae ad<»t,fic 

 *<iad«f. Etalterne (icutrt 6 ad <» c,fic <» e ad <» rf. 

 / h k 



Yaratletas 

 fe inuicem 

 teiminan- 

 tes quid e£> 

 Ccianii 



InteifeAio 



reAaium 

 pei pataU 

 lcUs qaid 

 efiiciat } 



X XIV. Vahrica para/ielarum circklarium pendet ah 



eodem centro , reBarurn ab eadem difiantia 



peripberiarum duarum. 



Teripherit quippe parallclx funt, qua: fupcr codcm centto 

 funr duct». Rcf/^ autem linet funt parallcla-,qux .rquidiftant 

 pcr atquales duarum pctipheriarum radios. Delcnbantur ita- 

 que dua: pciiphcria: ex duobus punClis refta: data:.Tum enim 

 linca ad contafluir pcripiicriarum duifla,ctit dati patallela; 

 vc cx punftise & /datx ab ducantur duat petipheriar ( non 

 quidcm intcgrae,fcd (atis cft fi pattc-s apparcant ) per cundcin 

 radium>J,inca c d dcfcripta ad contadiuB peripheriaruin, 

 crit parallcla data:^^. 



Fabrici pa^ 

 laUeUium. 



■^ 



Ali j fic cfFcrunt : Si in data reBtk diuerfa fumof centra,^ tx 

 iu peripheriai iqitaliiim radiorum dtfcribat, linearecla tangtns 

 ferifherias ent paralUla datt- 



XXV. ty€ejitila'atio eft d^ualium, fecundum lati' 

 tudiaemJiHearum produ5lio. 



Aqnlhta- 

 tio quid l 



Tom. 1 1. 



Eft itaquc accidcns linea: comparatum, vt vocant. 



Cc 



xxvt. $i 



