THE GOSPEL OF JOHN\15 YRAN( I\'5 T. VTETIJK l ARISIORVM 1,,11n1, FRANCJSC ' I LANGLOJS, alza;, ,f,èti CHARJ:BUSINESS, M not X[.),'1-CV.,\,f PlUVILEGJiJ REvJS. EMINENTISSIMO PRINCE IV LIO MAZARINO S. R-E-CARDINAL . How can we solve F. JOHN FRANCISCVS NICERON,AE>Anal'IAN. IN tanttìm Authoris vote Jèd also Work meritorii digna, . the patrocùzium encompasses nojler , Thaumaturgus . Projecting femel Cardinal : Eccui for animtts e/l of France that is not in c!ientelavzo E. T. Jpontanetts grant , who did not orgasm 6-l.etta /testimony to belief in tucefe action, qtti not fub tttaprote[/ione ÙtttS acquiefcat/ ù:tdigmu e_(/em whatever/ium prittilegio q110s in vrbe pri11cipe,ìpfaque so kings fede nac1us füm ,fz noneodem which noflrates affe{fu ducerer)mmo&fupra cttteros thing. 'TeFAMAper vniuerfu1n Orbemcircztmfert, mentts, bel'Jd-Jiciifque (enfum, qt1em video externiJ , dome./licif que,. how much per each though, effe common? E_11i'llnte10 pub/ica in the maam names of the fru./lrr:tfal/icitD, .who Japere poffe,m experience qttod ip{ecepi.with Romee I was doing. 'Tum of course you're not yet pttrpuratus fed purpurafcens, this ef} of all trial ç1' vote of/linatus to purple , him genùtm preeferebca who now fe re6,u buwanis exMbet fa lutare1n, qzti Gallzee vicforica pr,cparat & trinmpbos, who literca, Mufafquepromouet to immor..;,talitatem. I ùt Vrbe adt1ena season the purity illùu your admirator & cultorin portico accepted ,how mirtl with pnlc/Je"at the bottom of the ip/ìtu artuelogio &"1ntiquoexquifìt!ì & deletf!I meliorttm lihrorum mnltiturttm faculorum /the same,&Regummaximorum,exam..edine perornabca,not the main verb only cele6ritate,quanplum,queenobu Philo i/le JudeeUI nonfute ta11tumet1,m incredible your humanity 41timatU8 fùm to gttisfed omniumiudiciodiferti/Jìm11spariter,ufa·that's from me already then disappears,no one vernaculo published pientiffimuselegantil/ìmèin bttcver6a commfdaait;e had fPecimen buitu operu, the most famous your il/off {faum e!r togat& militù: arsenal Jponte commence, not redempturra scrap & cheap worth any price oh so good to the light& dignity , oppignerarurus mind M(Ecenati the best & the jìderabi/i/fìmo. Ah together with him of course at the time , that doesn't poffum jìne prttfenti a iuctmditatisfanfu slowing'to smell,' vindicate/li let me give you the whole love of which glass my occajìone prttrog-a/ti , &· vt altirn dt? 'Operu meritofèntirem, your coUaudatione and iudi-, do prd/becomes;Jli. And certainly more in eirn fcieNtite co •ni, il fM1 oeJ'lfOV '111 /A-"'}OIP, n,O" 11,EKOIVl"IIIIUllC, qnidem nm eJlicitur tantttm vt Jua prttclariJfìmtt anal dignitca con/let, fed as pr.efans and perpauum protrude Regi6rn ipjìs & their curatori6u, too commonitorinm, as in gtatiamfuam tttnt.e noble• ban & ef/imationis art recipia11t: .fl.!!!Jlt you _ _ori ;[ed ji Thaumaturgus 4r!JJtrlot!Jlèélittevndex om11zb11s, cuzRegzs ed11ca paddle ,lines 110s i11tludimur;t11.faéiis ;,011.circN ·· .; ' tio imps"eretur;Pcper you go!liusingenitiadmttxima fcriberis ; in chtttta ludi1J!US , t. in Q'{f.,P;trH.._, qutttpte_ arranged irinobis.sure.f/ìmèpeifuafum your benefaéforum cbttra'éleres mfcu/pM.;-·,m., e/I ;or defut11111m by you /when the art nobilijfìmtt, libamns on the plane , you [upta cr.elam in· p!erJo -tete'y. which./ìrmatur in all iudi.i.m , grau_iora beU! nitatem pe1114.push; 11.n profìci: no/Jis _ .load.I!. fl. moments librantur, deleéfabzltora pac1s hlandzmenta condiment, the price with the King, ruum of baptifmo (using it, of worship alumnum , firm e.lf colluf/uncommon, as as dtezjìdus alzo; etz.'/?1.1!.fo with 110s & ineluélabilis./ìdncia . .fl.!!_.d not pote.lf,vt i!weighted firt merit , your options./ìcio happen without your g!oriabunda Ju(fragio ttteri fe po.Ife conJidat place i!li fplendidijfìma in porticaeediitm tnt1r11m the third part of the iu/fus .ej}imator affìgnabis. EJ} i/la is not apotbeca , fed Ciuit.as version erario GaUiamfelicem&happy effeci/Ji,and in the days of el/ìcerepergisnullisfumptibusparcens&fcitntif/ìmum diligent.f/ìmumque man (Naudeum dicoditttt ipfius Bibliotbectt curator) adbibens, Anagrttmmati(mus. I o A N N E s F R A N e I$ e V s N I e E R o N V s. s E N s I s N o V A N V N e RARE e o N F I e l s. Di.fticbon. Q_u,1, never f tUlis once confi/Ja peraélis, lvVNC SENSIS NOV.A RAREmir,,.CONFJC/S;irtt. AL I VS. FATHER JOHN FRANCTSCVS NICERONVS MINIMVS. IT RARVS, THE SENSIS NOT COMMYNIA NVNC PERFlCIT. Waters.Sexdis 7. Kalend. On April Last Year .&e.e Chril1. Ml>cxxxvu1, BJLLON. IN MATVRGVM OPTICVM. R.. P. John Francifci Niceronis. F.FRANCtscvs OF LAN JUICES, Col!.At least I think. & Vi( General quifupra. Room + Seal. Cenfura Theologians Of The Order. Oh sainfrafcrìptiOrdinis.inimorum Theologiexmandarisfu )?enornm v1d1mus Opttcum Thaumarurgum R. p, Ioannisa. _ Franc1lc1 N1ceroms that so probauimus, vt not folùm in eonihil contrafidem orrhodoxam,[ed many comineri new, pra:lo digniC.a fima,which:Perfpeél:ma11;velfac1ho\emred.ant vcl prom,pueanc not finemagna voluptatecummenm rum eyes part:emur. Given the 110_fl:ro s.Francifciad PlateamregiamParifienfem Conuemu V I I I. The ides of FebruartJ,in the Year of the Lord c1:>1:icxLv1. F.aMARINVS MERSENNVS.a F.aAMBROSIV s GRANION,from Proximu.< w N /CERO are fourth century bc the name of the fìc er ili,, m fàllor, the next eloq1eio . . \'; t,mien eft C IC WILL be you major accumine /ingu.e, And omlormn acù you N ICE R.,ON E minor. BEL IN Sccretariu1Regis. JV'PRIVILEGE DV ROY. of Parlemenr, Maiftrcsdes RequdhsdenoftrcHoftcl, Preuoft of Pans,ou L1eu Prd1re RcJicii.:ux ì\linimc du Conucnt dc la Placc Royalcà Paris.lntirulé THAVJf1.ATVAe; i.s opTIC1"S. diuìfé cn pluiìcurs parttes, qu'il defircroitfairc imprimer auec (are fi.'l"urcs-pcm:J.onncrcccurieux ouurage aupublic s'il us pla.ifoit luytn accorJcrìa l)ermillion. Etfur cc, we lectres necciTaires. A CES CAVSES. dcfirant con:nbuer à la faciliré des ìcicnccs, & infirnll:iondu public. Nousauons permis, & pcrmettons aud1r Cuppliant Imprimer ou jai re !mprimeren thing volumeou caraélere qu'they iugccaà propos got it made! liurc,but en langueLatincquc Françoi!'e avec fcs figurcs, vendrc & di!lribucr icduy last le cemps of [ept ms i comptcr duiour qu'il Jcra achevé d'imprimer.Pendant !have equal! remps us fa1fons cres cxprcffes deffenccs à tomes perfones of quelquc qualiré & condirion qu'clles foicntde l impri1ner ou faireimprimer ,of\c \-end re & dt.frribucr en •ucun lieude nolhe Royaumc: & lit!uX d'obeiffancc foubs que\que pretexteque ccfoit, correùìon aunmention changement of titrc, clcfguifemenc, des figure< ny rcduéèion of great.petit, ou autrtmenr en quelqt1c maniere functioning cc foit 1 fans le confèntemencdud1t cxpofant ou inement t>: paiìiblemcnt cdfant & faifanr ce!bring your tous troubks & empcichemens i alns ,Hl contrai re. Voulons en outrc functioning mettant au comrneoccmenrou l la fin dudit liure wppie dc Lt prcfenrc Perm1!Tion ou v11 cxtraiél: d'ice!Ic,il friirrcrHlpou1.:bi:n .. dcuCmc:nt ftgnifié, commandons au premier Huit:.Jì.er.cu Itself!gcm 1ur ce rcquis tairc pourl'cxc:curìondcs prefentcs touscxploiéls nc _el'.LAlSIR, Donné àPans le 12.lour dc May l'an de grace, Mii !ìx ccns quarante•e Vl G NERO N, .And!ieué d'Imprimer pot;r lapmnim time le i,, d'Aor.f/ 1646, ELENCHVS E O R V M Q_ V AE N I H O C WORK CONTINENTVR. PR.h'.'.FATIO READER TO STVOIOSVM; Vl,i of the authoris c011jilio, the title of the work, àufdem fì1bìeflo, order, & \1tilita• you diffiritur. P R A L V D l V M G E O M E T R. I C V M. TO HVIVS THAVMATVRGI 0PTICI,SruPnfpec1i11.tmCurio(.e intell1geneiam &practice neceJJanum. the previous page. 1. OF F I N I TI o NEs. l PROBLEM TV M Geommicorumconflrdlio. The FIRST PRO PO S l TI O . .To date rdram line, from the given [pa. rio i iamparallelamfeii .equidiflantem lead, P R O P O S I T I O I I. On daram refiam line , & from punflo in J it given refiam line to the corners ref/os exware. P R O P O . I T I O I I I. Datà reEià lineà from prmflo 1xtra that given, the next line in the dar.e perpendicular deducrre. 6 P R O P O IF T l O I V. Mode aftignare, 'fUO Jeprehendarur, t1n rdla line to another inf,jlt1tperpendiculariter,feu to angulor reflos. 6 P R OP O THIRST O Y. Daram retlam lmeam in AfeDcent&ina BE ref!aalmefUpaBE, wl w DB adBe, itaeffe TO to ECadico w FROM:at :+•. I BE R p R I M V S. ) sPEllitk';.T "nlllarra lem d :,1r dise:.b. 'ddJVI ,f.d ;a e tne,tn '!f'.:af t:o'i'c:;.f!.:;:::;:1:/:::it:::.eacrualanum not aumuanr, ,tut m. puncu damp nerhodi exbl.·,uio cA, JUIM I riem adht/;e7orum regularium & rxlnbentur qu,em. 4mra mu t'}omua,porye rad; & mdttctns d1agrammara. '-t ejl E oh um .e/ line conrmuant •nemt's a Geometric ']'1lnfie caalia fòlida regufària compofita, trregularia, A--lme{fura: ciui/1 addttur met o us prapopa o .uapunaum B, bag .. oh . adGCao.s .a ana1 d e.ae<11onafum,tnmr111e In FROM, punc'la A (:ì B ; fimi/trip & in e D'fUn{fa e F,a. ,.r. s it D,BE, F A,B C,0-by jìgna mter(cffionum, line HG: tell ipftm /fapar.t!Its'-1m lme,e CD. OF F1 N I TI ON ART. A X I() MA I I 1. It mai:it e;? the detailed olwfl1 fimulacl,.·um, 9uo fub ,,,., 1 A X I O MA X I I. !baQuidfìrrears m P i ejl reiucl1u •pfumplanum attin!"itrJreé/rn.:aIl E Lines & pun{iù 'juibm i11 and P NO T A N D A. Cm:a conftrutiiorrem P R: (:} P O S 3 ru/1 t a T I O I. Given pHnEJa fuper pla,mm'. ezuhueadiftam1a àfcenog-,afhwtm1 e11wpunéfijitHm m d4a pltmo Geomerriçq, altifaaiolfe jimi.liter J.ttit "faMtnta anger udtao emm,oejèua ('jue to B N, & à punélo F,the line F G same FROM the parallel ,fyead line B C, will be I H & F G mrcr fa a1uales (:7 a pair of,he!.t. 6 7 PLAN of O X X. Given linr.e altcuius fìue I?iil!m, jiiblimis by pendicu!ari height fuper plane, 1pjìus Jcenegraphiam feu almudmem apparentem Jecundzìm fimm 9uem h,,bet on the board to find. 6 7 PR O PO THIRST O X X I. THEOREM. Vte ft almudo eyes Juper plane dibM ff,h.eraliter jlellatifiguram in jèélione anarentem defcribere. PROPOSITION TRIGESIMA FIRST. Sccnographice'deli0unearejèu to proj}eEl-um adapt (from (olida, jlellas, 1uarum rays imùsuplani, exterizìs 'l>erò to the pri{ maru pm,am f nr acute about c.trero fimul anger connexas w globifiguram )>zdeantur express. 97 PROPOSITION TRIGESIMA SECVNDA. So/,d,cuiufdantpentagonis pyramidibus .1ualibus, JJ,harafirer flellan the figure on the board apparentem delineare. 9f1ue to /1 • neam horizontal, fa hal,_u,dinem ,ipparenrem ciufdm'. punEìi (u r to almuuPROP 0S TRAVELLING TRIGESIMA .INTA. D1agram11wa cl'udam Architedur.e mdit..irisJrenographzcè outlined in exh,l,m. 10& FOR THE POS TRAVELLING TO BE NOTICED. Data In ra/;u/a fèujèElione cu6um the am neare. lt.e.e reft,e DC & F E, ha _(ecabunt line BA tn the same punflo G : 'l>el dtculartter in the strict sense rec1o plane Juper 'l>no S 1:. V p E R S slowing H A V MA T V R-G I O p T I e I firms exhìbeat. Mo while 'Vniuerfalem aJstgnare 'iuo pofsit image FOR POSITION IX. jèu conc,1u,1m opuco geometrtcè conjìgnari , it,t 'l>t , etjì we from dirello to the flat, the 'luibus delincatur,ajpe{/uconfù(a & deformu apparedt; from the determined nihz/ommus ptmflo amended ; well compojìta & protorypa Jìmilisdffdi'Cdl. Ij8 p R Q pO$ J 1' J Q D E Cl MA. 1vfodum "l!niurifalcm rradm: 'JUO pofrìs brts. Pr.tj,élzo of fabieflo l,uius book, datiJìmulachri [èu shape cui11(cunque, in the 9ueMet cxpojìto plane Jìue fuperficie mobz/i regular or zrregulari,jìue cttam in several Jìmul fuperfic1ebus mobiltbusopnc,,mproiec1uramjìue dzrc[l-1 fìueobli'l uiafj;eElusorganicèinjlitue re; so )>t from the given punRo proto0>pafmilts appt1reat. I 65 PROPOSITION VNDECIMA. To deliver mode 'l>mucr[alem 'fUo ri,u [eéliones, Jemper tc1.menfia e,tdem '1>;fo,_{eu ,1pp.11-c/;tt e,ui,m 1m,1go (.'."& the same obieélum. pofm o b1efli rniuJcun7u e of a given imagoJìuedireclo ,1fJei1u view, Jìue oblì1uotJjeé1anda mtuttu, in quamcun1ue expojìtam fuperfi:1em regular or rregularem, mobilem or immobdem,irmno m plurcs j;ignorance & dwe,J,ts [uperficìes from (cenographia: legzbus orgamcè tra1frzbi farmem, \!t oculu outside due jìtum collouto diud all no ,1pf'1rec1t; 'ildeatur yet rcjòrma ta & re.ula,·e <' p:m{fo dcterrmn.1to. PROPOSITION DVODECIMA it,t W è proprtopuntlo à-I6 9 AND VLTUvlA. How PROPOSITION 11!. }vfaÌ1odumapg,to;-e,7ua po(,1s d.iwn 9u,1ml,bet tmagincm in a plane oblique proiicete, 711,f from the dire,:fo 7uidcm afyellte nul/1u,-thing sure jzimlitudincm by Jc reprlffentet; atex dercrmmato punflo & a1Jeélu obli1uo, pe1feé1um event of any /mmlachrum exlnbcat. PLAN O !V. In extmori feu com,exa contfuperjicie,d,fcnberc, 7u.e, af, al111ndc' confuf, dcfòrmis & improi portionat,t ,,1c/c.m,,-,,,if,ilom,nùs m due jìw & è'punt1o determinaw conFfef/,1 o btc[io propo(!'t,, m plams fuperiorurrl cvnt1gnationum [upcrficicbus, obiec1apropof,ta jèenogra• p!w/ d:imbrentur expancre PROPOSI TIO OCTA V A. To conflirutumfolis lumm rxpojitoru . ti1 confliwrus fupponir11r. Q11andofai beyond the board before the eye, intun1. PROPOSITION SECVNDA· From daro l11mme propoj,11 p4r,tl,cfrp1 pe.li vmbram in Ji1bic[/o pl,mo dejùme. l ROPOSlTlO TERTlA. From afignato load:to prevent a given match.llelcp:vmbram in fubieélo plane ,,d,miemre (:7 fcm.;r.1ph1 fienogr,,pl,ucè of/meatu FOR POSJTIO QYAR TA. From the given l:imine P"1'o(,'u Tarc1i,fri da:nafcebatur ,received. Parenteshabuir, inrer honoratos citizens, & mcatummultitudine not less than qu. dignitare; pra:cipuos. Father Claudius, the man is first of all kinda, prouidus &follicitus;MaterRenara, e,cBarbierorum nation vetufl:a & bright, especially in the ingenua , foorum loving & generous, iupra foxum fapirns, strong, & animofa, femper taking into efl:. And has facilè dores, in primogenirum 1uum Ioannemnoll:rum,right ipfo natiuitatis & love, ve in the pledge farre chariflimum, & beyond where: fperabanrur with time nupnarum securities, enjoyable & loveable, tranfmiferunr. At home for the first time in the fans, lub best of parental care, piety amorern with laél:c fuxit, & dome!l:ish exemplisadcapeffendam virtutisviam, vtper a:entertaining inualuir, exciratUs ell; which vt fu binde acceflit delcél:intermediate of such ci· uitate pr:rceptorum follicitudo,wonderful dl: quanrurn , within breue rempus, nonbenè haél:enusexplicita character,ardensalioq11ìn &viuax ,to all moruminfl:ìcutionem& learning education, through prn:cepta, profecerìt. But, cuminrer parts themselves: hardly numerccur a:ras she tenerior not I'll go through veihgia, which ip(e to pcrfcéram Gra:ca: &Latin: the language: knowledge and exquifiram human lirerarumperceptionem, progrelfusell:; nufli from condifcipulisfecund nulliexa:mulis odd, it politioris difciplina: curlum confcc1r, Enimverò·,with marurefcenre fenfìma:tatc,to deligrndum {ìbi life: in perpetuumdeinceps retinend:r class, by ìntcnores il:imulos infl:igaretur; rra:ualuitpietatisfl:udium that abvterocomb1berac, omnibusillisfortuna: ìncitameritis, which: won: domiopes, comp,tra• ta: talent &laboreartes,fuggcrebant. Not fuicilli deliberate, ifcend:uninfiirurx pcrcumU1!ììmca }bauer;.i.c acferiÒ at perdm nuand1opcris which-;1111viroamico & HLtdtofocornmendauit ; with the terim ipfc polt m11lus percgrrnationcs, by lt1mmos & inrolcrabìlcs pcnècalorcs ,_ddarns 111 l'rouinciam, ImpcnJ Ga.llici ardcnri/Tìmamr1·g10ncm , fcbrc contracl:àm, in ob/èurn &. cheap Porreriarum Conuenm ,not far abAq11is Sextiis, pniculofìilimè ,\ccubuit. Nccmmora, e: 1llo rn!.urio prupcrancer tcducìm e. Ao1uas tra'1f1 nns, vbimprornpr,r tì.1ccrnTe:·ent re mcdi.i mhil d{i quinofl:ratempefl:ate in hacce bezel:fl:ra plaufum aliquemmen.a:molisponderi(que corporibusido1:1eus: huiufmodifontLibra, promerentur,veinfìgniorespra:ca:terisinnoftraciuitate Parifienfi S.u Vouet piél:or royal,L-De la Hyre,in Italy GuidoRhenus,Peter àCortona,plurefque others whom nonrecenfeo,maxirnè cercè because &inuproiiciendisuineamentis,ininducendis colors,inlumine,vmbrif m1 pveame_xuma mudmes,ufyderumqueCLI. 1mus icicn nz pI1a:nomena ritè,dhmet?Qu1dnacuralisPhilofopecunus,Opttca: du.c>um · l11·a;,are not".b . Archiceclonicaacem,commodu evcm experune arsi·11a1n• fignisadpra:cipua rt1ax1me.necelfana1lh.scogn1.ìoeH,cu_mramecn alr it prdpt'èfìnri..e .e!l:,plenqucabh?rreanr: exilhmabamfcilicethacratione,prdfofiris'ehumfmod1 fubnhranbusadmrrand1s,poffepulcherrima:ftlenti±èon;ciliari, quosalioquin ipfìus vtilitas furnma&rtecelfitasadfllt lludium,e& dclìdcrium not percraherenc ; gpc, namely vcn1m etfe arbìtràbaiquod called. Everything you/the un punllum, 111i mifcuir \>tik sweet.e poGcadè,vcfolida,eminenria &farre dillìta repra:fentet,which: would otherwise be a flat,a:quabilia &in eodcm plane fìmulrealicere.iflunc; Whereupon& with PliniumZeuxis a great reference gloriamcon!ecurus, t1uodevuaspinxiifet so much trade, vr dccepta: birds 111 casaduolarent; fcdmaioremParrhalìusfìél:o & adumbrato in rabula film q nod rcmoueri Zeuxis pofiulauic, 've piéturam quamfob colatitantc:marbmabatur,in{i)iCeret; greater certèipfìusZeuxidisiudicio c1ui palm cef.fìti.g_enuo shame ,that ipfe only the birds fofèllitfcr, Parrhafìusvero ieamfìcem. And bune we perfeétionis & abfolurionis level uurcificumnofirorumpiélurisdeGdcramus; fonrncmpc admodùm few who 1llùc.mmgant, quiaplerique opcica. pra:cepùones& The.10gr,tpbia:praxcs &mnnis kinds of examples of the propo Ha:c was igiturin ipfo fofceprioperis initiomensmea: fcdcufi'.t ali-'when some Perfpec1iua: authors legcrcm, & them przcipurlec1uiregu!aria bodies fcenographicè delineanda propofuére,animadncrn ahquos, vt loannem Cou/ìnum, Samuelcm MaroleGumin ifii.crra.e, ncc focus or.horem of the book, whose title cJt Syntagma in ruo \>ari4eex1m,47ue, &c. referti qurdem fìguns fcenographicis c!cganrillìmisifed rules & pra:cepcis empty: it has the folummodò brcuèm one difcurfumdc general method,how to, cx cm silicon gratià, pyramidi feu T ccraedro, ve pote corporu fimp licif!ìmo pra:figic & applicac,necfìnegrauierrore, vcamplmspacet from Iv propolìcionis 'vigcfì m:r certia: the first book of the party: vndc fa cii è adducor've crcdam vde ife another aurhorcmdiagrammatum& aliumpr.rpofìri difcurlùs, or not a few erroresin fcquemibusmulro lànediffìc1l10nbusiconifìnisìrrepfìtfe, although we do not inuenufl:è defcripn & adumbtaci seem-. but of those fcripferunc .rnthorcsalii, ve! ipfà dclincandie merhodos tradidère adeòabJl:raél:as, vrGurdus Vbalclus; vcladeò iutricaras, that made Daniel hit points, ve cas in vfom adhibcre cyroncsùxpoflì not. Are dcniquc aliiqu1folidorumlmiufmodiproicébonibusm plane mJl:irurndis Gngularia inltrumenra proferunc, fcd ifiiu, orgamc.r proicérionis modusrcgularibus pcrinde and irrcgularibus .1. quibufcunquc bodies&obicél:iscornmunis efl: As cx no{ho Scenographo Catlwlicodeprchendet, c1ui kgcr: the trouble with in this rnihi ipft fatisfoccrc optarcm & other ctiarn prodclfe lì poifcm, fìngularcr . {ì cuiufquc conftrucndi & delincandi rncthodurn cx verts Gcomctrtxprincipiis & Sccnographia: pra:ccpm concinnaui, adding criam adolccm proyolìrionun1 Heart':IL;ri1s, v61(ì what aliispeccatum effearbitrarnslum,proprùcenfuranotarn: ,1ua:nuncommapublic:t ftuh J1 Trip comp:anger' while Jl:udiaconccd bq, penu muenca depromerem &iaminuenrishaudinfielicire1\al.f re)inquiinus. Ina.lceriusaut.m share book quirtertius will work to m1randas fpeculorum propnetates & pra:Jl:an nllìmas in detormandis to it.em fpe.u!a reforrnand1fq.e from the given punél:o images proie. él:1orubus acc1p1es ,fì God fauent, ormmque &viresex eiusimmenfa bonita.e foppeditent: ficut & fourth book,quifecundus eHeiuldem party, abdica rcfraétionum frincipia opening, & cultivation fìn gulares demonftranonefquem exlitbendis permulciformia diaphanaomnis stock photos exponenrur. In omnibu.but him speaking charatl:erem, feu fl:yli kind of confequimurquodmaterix how tratl:amus especially, as for instance.the us, conucnit .i. not elarum not foblime or mulcum elegant, [ed fimplex us excellent qu:rdamcheoremaca & cruditas demonfl:system .uod to oh.you'll be able to infcriptioncm attinct, it Thaumarurgi O pticirnomme mfìgmendum of my hearers: with cnim to Thaumato-pocticam vnii Forums pure, as feuerioribus di[ciplinis inject to vrilirarem belongings; in which vraitSencca,mind fcribendume!l: not the ears,r nè this option warns Clement of Alexandria, them quihxrent ditl:ioni uerfalem, fiueinrer Wonder of Mathematics referanrur Spha:r.lidonii, which:ccelorummoms, phnetarumque conuerfìoncs & fingu bus & in them font occu equal, things ipfa: flee. But &aducrtendum ell not all internet à no twice in this operer laP.hxno111enaccelethar.prxfcncabat;Architxcolumbalignea,qux leu1per air volacu [.onte hovering; great Archimcdisfpecula,quibusmoppofoas holhum cla!fes, fbmmas & firefox inuehebat; ma chma: qu1bus&ipfasna.esincegrnsin almm stil,l.holi, just in profondu111 dcmerpebat;omma Da:dah Auromaca ,ipiumque Alberci Magm mdulh1aco?cmnatumcapucxreum that vduti namralibus inll:ruél:moisture.amsloquebacur;ncc not & ll:upenda doél:iJTìmi Boetijr proponenda frriél:as geometricx demoull:rarionis laws confequi:inrmultis for easy cultivation & got them methods venamur potiùs, nq uam,iltaomnia esagno,cuur:m musenimpartis first book, pofl: hands cnpt& éèum work vchmlr PRLELVDIVM TO PERSPECTIVES CVRLos:AE. hcndirur:&huncquidcmftneerracistib1 rraderc as much as pocui conarusfum,(cdopcrarumi1:curiamnequc abfens or prxfcns cffu_ gerc poru1, vrnon ali,1m iubindc & destiny deserts, bpfos irrepcrenr; ar 9uo grauiorcs eominorisclk important exifl:yes, faciliu[c1ucpoilè from inrcllìgente & !èud101olec1orccorrig1;any enimnon aducrcatpagmà179 le_[;l debercauthor,m p.·o anrhorem, [ubjìuupro/ubcifhu,s; paginàIg quxfingdlarnn record dfcr operxrcdu1rnlant1s. .apropter prevent your Candid Lcdor, abuc1 mouth o vd pcritixd1f!idcrevidear,not tcdiutiÙsin rlbs to stay; tuvcrò fìaliq.em INTELLIGÉNTI AM AND P R'THE AXIS PARALLEL TO M' · I MURDER.SSARIVM D E F I N I T I O N E S. V N C TV !1,i mathemar1cè even with Eudifon, has. i.Elcm. dclìnitionc 1. cxtcrofque Gcomeuas di-ornrid cu1urnullx font parts, feu that.eU: indiuifibilc & omms cxpers 1uancitatis ; attamcmrv. of co now agrmus rcfpeéhuc mm1rum & when.oh.r.tnc to activities Perlpec1iux pra..::l:kx & amlicia!ù:,reél:è illuddefcribimt1scum dicimt1s fignum any mini from tremo pens autprxacuciftylivertice in which:unquc fall:um furnhnc that ind1uifìb1lc even appareac fcnfui, lit ramen reucta & ,ll,!è,lutcloqucndo,vt pote foam habcns quancitatcm & cxccnlìoncm churches, in partcsinnumerasdiuifibilc; ralcpotcfl effe pun(ìum in the first tabuli lignatum number I. Line but with cofdcm Gcomctrix fcriptorcs definicur !ongicudo L:nrudum cxpcrs: fèd ncquc ha:c dcfìnìtto conucnitlinca: naturalitènfibili what kind of in the art Pcrfpell:you.e delineationibus I address to indeed bui_cfìcuc & punéto quanticas any fcu latitudotribumda dl: anger as diuif1bilisfit quidemrealitcr & abfolucè; indi11ifibilis still home,fcnfum, so much for iu!l:greater fucccdet in ciufmodi ddineationibus opdictatorship offered to me, 11L Hcptago':1us who fcpté as diagramn:ia 19. O tl:ogonu. who eight.En nca·gonus qu1 noue.,I.)c:.agonusuqu1 ten;.E.dccagonus who whereupon um, Dodccagonus qut duodcc1m& {1c JcÌf éf>tlmain Iibn pnm1 Thaumacurgeprò..li!J;ufccc<>n!trutl1001s rnci.ç,ctumeq.am potm n1m who àd &tlìm d11p(uM reb'}to 11nguh! & clrcul?m defonlm1do :about ipfum criangùlUltl, qu41 fa.<>òafo1 fr.d1&1 mangultelatuse cric pentagon eifcmc1rculo mfcnpn. Fadms still the same v1dcturptnfc prliltlri .à q111m pnd'cnb1t method Albmus Durerµs 1ib. A, fa.r GtòitiCtti. but because errauit ipfe D1.mrus faciendt1 .entagM1u1n x11uilamum fed not requiangulum viap,è demon• ll:m Clalliu11ad pta}'ofititmcm :r.jl !ihri ou:aui G'oometrial fux prail:ka.e; qualfi à\!ttln Éutlidès reports citata p-ropòfìtionc u; rclìe eodmt GlaHiG.ttl ptò.hciot1em ,iltimam lib. fourth Elcm. longani ra anguh CA D c!l: quamms arc CD cx centre A dcfcripti interccpta uttcr hncasA C & TO, discovering how many gradw auccirciun. ferent1a: parts connneac arc CD, fucile: crit quarttitatcm anguliinis dt arqué diffìdlis, hit us an èur\1 110 fubiung"rc practice a certain fadllimam which vnà t:ademque op.rà Ptolemreus lib. the first magn:t cohll:tull:i{}appurtenances in tirculo given infcribit the pentagon &. decagonum xqmlaterum & xquiangulum. Is ieitur in.dìagrarnma.:. you 2.6 tabulx this first: circle darus FROM the CD in which the pentagon or decagohum a:quilàtcrum & xquhihgulum you would like infcribe. CA D pronunciare:.tverograduum fcu parcimn circumfcrcnti. {Ìr arc C D fciecur this way; fupponimus giue the first encounter lincam TO vbidelènbiturarcuscirculiigura: 2. 4 a:qualcm dfelinc:r fcu fcmidiamcttOe A B.figurx 2.7,which pofitoiùmcndo cirdnocomtn'.lniin figuru+fpa•components of the fcu dillantiam DC I eiufmodi circini apcrturamancntcimmobilt lbcuatur one il!I'm pcsin pundo B diagrammatis .7, a second cadct ". rc:diuifo the first circle into four parts xqu:ib by two diametros imc:rfecantcs you borrow K at the corners of rc:él:o5,diuidacur dcin m11è m circumfe1cntia fupet level quadragefimum fifth, gpc,:pc ficc as the angle CA D cognofcatur effe 41 gradUUl\1.Brcuius adirne & faciliusidcmpra:llabit quicunquc vfum callcbit faél:o vccunquc ui' diagrammate of femidiameter K C documents on the role of xquales the pun él:o E, à where vtlut center, inreruallo the F.B defcribacur circuii arc B F whose hy.oten..fa fcu string F B will latu. rc:quìfitum pentagon quoti in penphena pt:ediéb circuii circunduél:um à B in G, à G in H, by H ll1 I, from I in L from L in B prntagonum formabit xquilaterum &a:qmangulum, that was prxll:andun: but the line F R between cxm:- mum arc circuii & punél:um of the center K comprehcnfa em lake of the,:ago11i .qmlareri & xquianguli the cinulo infcripti vt from fìgnans btcnbui HD, DI probahti patcbit: this aucem praxeos demo:1llrat1ònem Geomctricarn have that volct, confultct Clauium 111 lcholto to propofìtioncm , the book of the tenth tertij Elem. A P P END IX. circini proporcionum this rationce;2 4 cx the center of A bow CD, transfcratm line reéh l I D or A C in linc-a-dtui!ionis circulormn feu strings to the aperture .the numbers 60 ( hi. efl: nunicrus fem1diamecri circle) fumatur qcmde comrnuni dividers di,. Jbntia CD, transfcracurquc to duopunébin dividers proporl.'ionum ;;rqualitcr from his center difiita v. g. in paradigmatc propoiito fì. gurce 14, pofità lind. A C to apcrturam numbers 6 o on line chotdmim leu diuifionis mculi, circìno proportion mancntc immòto rcperictur diflantia C D,apertur:e numcci 45 pcrfcél:c congrucrclìc _quc potcrit cnunciari angle CA D 45 degrees ,oncim:rc. H it pofitis princip1is & fundamcntis not erie dt/lìcilc: tx to those given cuicunquc circle polygona qu:euis of hell shall bere, li ca ses priu.1pforum of the center angulonun quanticasinnoccfcar; font autcm 1.11 quQnis polygono feu shape flat multorumangulorum&: same mangled body was, the corner centrequi.,à duobusrcél:it lmcis cxpfìusccntroadduosangulo5eproximos duél:it contincntur vrm fiera 18. .ngulus ceneri hcxagome -lin,". .. • , .ig· nc_ftu,tùbt.agtaduum u.o mcnc.lo.,seagull tllnia..IUicfdM: htcUW 1afcript1 : f1ca 1J!!l"411t1 {Ì by the bti.c numcrum diuidatnus ; , o• cenum c:fi of di. ùilioìirs <1Uòtitntcm forc 71. pto quantitatc corner ceneri fìagu r. fupradi.a: f.u;c.tagoni, quamobr.m fumpto qui_nquics in pcri fhtrià afdUl ipàCW degrees 7,1, , mcer ha:c fpat1a fignali>untut puodl:a quif1CjuC1 q. by rcllasa.onncxa lin.as pmtagonum rcguNH ft;rmabìiiit 1tq1mmgulum fcihcct & a:qwlarctum. fim defcriptus eodcm inrcruallo fcmidiametri A B. diuidi::atu• ià. tr1 polygonotum by rcgulam pra:fcriptam ncgligcrent inquirm:, no1;1em fartes from:qual.s in so many v.dclicct, ,.antiutem of those in pr1:cipuis fi.it here fubncérere: anau!us ra 1nfcribcnda contmct. Sccabuur aurcm q_uadrans BC inptopofi. Pétélt & of lif.fem foundations the same pra: flari work circiniproflòttio1t1tm-, pofìtà cnim fupcr inftrumcntum in lineadiuifioniscirculorum fcmidià111ttro circle, which infcribendum crit polygonnm, to :1perturàm numbers ,o from vrraquc side, aperture nurn<:n refercmis quantitàtèm corner: intcrioris f01 of the center figure: ddèribcndre give l11t111; tiufdì:rh shape:: easier td capitmr from paradigmatc in fig, 1. 6! fì cl\im {btuatur fupcr inftrnmcntum in the hnea chordarnm fcu diuifioni& ciri:Ulòrum to the aperture numbers f;o femidiamctcr KB feu K C èirculi FROM CI H , dividers manenrc immoto aptrtura numbers ;1. give B G for lacere pentagon cidem circle infrribcndi. Nob.s aurtm vifum d1: for those who ciufmodi corners intcriorcs fcu ccn . fcribendis abund. destiny to .opofitum nofbum diifcroilfe. because yet .ummcl ncceff.r.a & mainmo fu.ra . v.ui in feq11C11ti6us, rrzfctt. with dcfohd1s agcmus ,huummfqipno, volwmusùrgra. gel ftud1oforum & appcndiccm hancaltcram fcuamcthodurnipfn infcribendi by quadrantcm circuii , that inftrumtntaqi ·mc 0m,. as to who vetfanrur in Mathcmaticis cft at hand, cx Clauioqui cam x1me,needle fac1btatcm a & vntucrfalcm in omnibusmqdum przfefcrat, cli: autcm huiufinodi. So v. g. infcribcndum citculo diagrammatis 17 Ennèagonum z. quilatcrum & a:quianguhnn feu shape noucm latcrum &: from.o• rum zqualium : fumatur giue the first encounter i!liw quadrans A J C vclaliudèoi of the center triangoli is indeed exquisite gradual u.o ; square vcr. rcaus feu degrees 90; pentagon fcu fiare five sides. xagoni feu shape: fex bricks 6 o ; hcptagoni fcu figu ra: feptem làtcrwn if ; fo.ogoni fou lìguri: oél:o latentm 4J; Enneagoni feu figur. now:m is widely used.rum 40; decagoni fcufiara:dcccm latcrum 3 6 ,&c. C O R O L L A R. I V M. Hle .I will be not .ft pra:tcreundum for inièribcndis circnlo in the strict sense. , . . tc_tis polyg !nts from iv propofitionis .exta: h.us pra:lu,dtJ tnfi::n.t. liguraquacumquc requilarcra & a:qmangula mcirculo, aham factlhme r.lfc: inf.iE,i in irodccn circniu 'Jlla: habcac latcra. uplo more, dtutfis erenun bows including battered fubtendunt bifa ram,from&c. gpc qua4ttc·cx qu-adtato in cittulo, defcrip. oél:ogonum pèr c1tatum heart.llari.m; e. oél:ogcno figure 16 laten1m, ;i., 64, 1-1.:8,&e. l taex mfct1pto d1a.mace1. cabulzhuiusheptagono lìgur".f 1"4 latèrum e'idcM circirlo qifcril;,emr easy, business fr bow. E P, Hi, .c. bifariìlm diuidantllt io pwfris H & I & rcél:z mit.s ·parts a:qi:.cs vcl cx i!s qu. fupcrius .iximu1 in the former be yearning for•• dice, vclopera mftrumcnt1 pamum vcl ct1ambcncliciocireini0Mn• munis dilatando condition the legs way more, way less doncic,rope,, rias comm difta.ness p.tiri q.adra .t.. in parts of the optatts,: faduuc emm quadrans m "']u.tm neceffeJ1t to co/J.oc411A11m Ji.jla,,mf p11nfl11m IIXl'fAtrabulam run out ; p.iucis dlltem h.tc a1'hlbl & /,l'fflit,r. f'"""f"'1iRi,.t nfirumenco mancnte immoto fomcndam effe aperture nu_ .mc:n 60 where: will be fcmidiamctcr circuii which infcribendum cric polygon.m whose side becomes the data rell:a line; example .forcaffis business fìct il Juftnor,1ll.dhabestinfcrius prop. 2. 7. de. the first where the body icofzdrit .1cnograph1am dclmeamus that confulc. Ca:tcra but as folidorum dclinitioncs &.other: work in decurfu intelligendis fcu con•t ,frrucndis problem necdfaria that we shall judge for the daughter of smoke cx.plicaturi why dc these haél:cnus. ·PR A:.L VDII GEO METRICI El FI.t