DIOPTRICE, 



five 



DEMON'STRATIO EORVM. QV£ VISVI ET 



vjrjbilibu5proptcrConrpici!Ia,hoccfl.vitrafcuCfy- 



Hallos pclluci Jos accidunc 



I. DEFINITIO. 



IN'cIinatio fupcr fupcrficicm, Aimitur dc nngulo inter pcr- 

 pcnditularcm fupcrficici, &: qucmcunc]; alium radiuxu, qui 

 perpcndicularcm lecat in punOo fupcrficici. 



II. AXIOMA OPTICVM. 



Radij in medium dcnfiusingrcdl rum inclinationc rrfrin- 

 giinturArcfraiih intra corpus acccdunt vcrius perpcndicu- 

 Jatcm rrcOam fupcr dcnfi fupcrficicm in punQo incidentis 

 radi). Iidcm cgrcdi ex medio dcnriorircfringuntur,& rcfraOi 

 extra corpus dcnfumd-fccdiintabhacperpendiculari. 

 IJI. AXIOMA OPnCVM. 



Ea Jem cd refra^io tcdibrum, fi vc illi natuta fua ingrcdi- 

 antur n vc cgrcdiantur. vel uc talcs conndercmur. 

 IV. PROBLEMA. 



Pcllucidi corporis duri rcfraQioncs artificiolc mcciri inc. 

 mm ra Jiorum indmatione. 



Stittrf-MdurHmfcltu-.tdum AE, li ttrminttUT uni txytifiti. 

 ftftrfatfUniD £, jY^»4W Jud 

 glut tngAHiHtflirthfofiiiet in- 

 ter [i ftrtlUU, CTfrton td tiigu- 

 hf reel 31, qutfi^it B A & E F. 

 Hitic eamf trs cifuU 'ne* q4:cHn- 

 ijuem.Utru, veUliexh\>.9, tuvis 

 foft'fuitt, frtjoiiu tktemret 



lOANNIS KEPLERI 

 S«. C*. M''». Mathematicx 



DIOPTRICE 



S E V 



Dcmonftratlo coram qua: vifui & vifibilibus pro- 

 pter Confpicillanon ita pridcm invcnu 

 accidunc. 



frdmijft EfifloU GtUUidei/s, qua f»JI tdilionem Nunc^fiJerf 



fftPtrf^HiUi, H0VM & *dmirtndt incxU 



defrehtnfg funt. 



Item 



Extmen frtfttiomu Uutnii Pent Gt/lt im Of tied EBtUdu^de 

 uju Opi$ets in pbilof$fbi*. 



AVCFSTAE r I N D E L I C R r M^ 

 tjfu Dividu Frtnci,' 



Chmfriuilegio Csftreo tdtnnos XV. 

 M. D C X I. 



T.t qiiiiimigoreivifihilu tfl everfi pemrrtm len- 

 tem : Lentvero t>r$pi«r non everilt denuo,qttod ticctftt 

 i RemolioriJeJfeitt tccifit ,*d tcukm trtnsmittit,ex 

 Jufftfitt. Accipit til tern rtJ^eHn rei vifibilu, tmtgine 

 everfam : Ever/im igilur rej^eilu rei vijihitu *d ocu- 

 lum mil tit. 



Etquix imtgeipfi rverfi, frofe prniSlumcoHiiir- 

 fm.mt/or tfftret re ifii, remotius xqiidlii ; & tdhue 

 remolim,minor,per XXCIK imtgoigtturhtcfic ever- 

 (t,ubifiieiit tmfhttt fer lentem fropiorem, duobut 

 frimindfikm ititjir oiHHtnoevtdel re ipft , ultimo cd- 

 [n vel Of jar veldjHtlis vel minor, frtut faeril lenti 

 nmiiilerfeproptrlit,(^intejl intrbiirie trlificu: eerie 

 ttmen mtjor.qaam qittaum lent.oeiilo froxtmt, e*m^ 

 dceeperAt k lemte remoliori.per XX C. 



XXCVIL PROBLEMA. 



Daobusconvexis diflin^ia prxHarc vifibilia 

 & erci>a,fed rrwnora. 



Hteduo eonvext oportetin fuffidenli difertmint 

 effe eoKvexiuium. Collocetur igitur kmIus extrt m- 

 trimjj puitilt concur fnum, tllerim pimilo diflinClio- 

 nit pnpior i reli^iipunOa diflmnitnii remolior, ul 

 ild neuiro foliidrio everfd diflmHe cerudnlur.Si enim 

 flier in t lenteshocjiiucum -oculo in edndem linedM 

 <ompofiie,cor^lrxiidvilid femutuo toUent, & difttm- 

 ^lofiquelur. 



Vl dttlem & ereQdfil imdgo, of oriel cdm lui euer. 

 II, El ul hocfidt lentem pToptorem oporlel ipfdm elt- 

 tmeffe remoldm d remoiiore ultr* lUiiu/unil* com- 

 <urjue. 



E i Sit 



•f unburn colligtiur, C^/hnt-veri vifi- |\ 

 bilidpunclu infinite. Infniu igiiarU' 

 lidpuntli pingeniur fuper p*fjrt, ideji 

 tatd rei vifibilu fuperficiei, 



XLIV. PRDPOSITIO. 



Pi£)uralcntisinvcrfacft. 

 Kdm lens ell bdfis in quam wfiflunl hi- 

 ni ulrimj. coni, dlieritu -vertex e/l in 

 punHo vifihili, dlierius vertex inpHnclt 

 finurefuper.pdpyro. 



XLV. DEFINITIO. 



Dicamus talcm bigaiu doOrin* 

 caufaPcnicilftiin. 



Um vera p(ni;i'li tmnet omnium 

 funHorum in lenle velul in eommuni hd- 

 ficonorum concntrunl O" trjnfiti lenle 

 turfiim divcrgiinl : firliunlurtj^ P^g'* 

 tonlrdrui. In h.tc picltird penieilli tret 

 funt AB,CT),& EFeoncurrentesinlea- 

 tecanvexi C H.veliiii in biji eommuni. 



XLVI. PROPOSITIO. 



Sicut fe habet Diameter piOur* 

 adeiusdidantiam .ilente, fie fe ha- 

 bet diameter rei vil'x ad eius etiam 

 d:flantiai!i a lento, fin" Nam axes 

 pcnicilloMiiu /'rccl.tdiin.ta punOo 

 vifibiliadpuiiriuin piJliiri rcfpon- 

 dcns) fecant Icfc mutUo omncs pcnc 

 C inuno 



No. 2265 {v^^ge 113). : .' ;' 



Titlepage and illustrations of this celebrated; work. , 



