^:^ r»' ^- II \ I TTCHON/S BRAHE A S T R O N O M I ^ INSTAURAT^ MECHANIGA, EFnGiEsTYCHONii; Brahe Ottonix)is Dani DNI DE KnVDSTRVP iT ARCIS Vranie.vbv'rc i.v INoNiiABERll l^ i\- SVLA HELUSPONTT! DAMICI HvENNA FVN D ATORIS llNSTVMENTOilVAK^AsTONOMrCORVM IN EADEM D.I5POf ITAFVH INVET3RIS ET STPA'CTORJS i^TATlS SVA, + O . AXNO DNI. l S" B^^. CO. \?jU ™|i|^|pW«iPPii;ff^ .-.' '.■ ,'1 '. i-J i'Ui; tliiJjiL! teMiillgliii^^ mmmmiEm^mmMm.^ An N O •■ — ■ ' '■ iii. ■■-- —~-.^^—— —»———< cjrr. D cj I, Qum Qdfaris ^ ^gpim qmrundam Trhilegiis, AD fiAVGVSTlSSIMVM IMTE- KATOREM RVDOLPHVM SECVNDVM TYCHONIS BRAHB TRAEFATIO. StRONOMTA SCIENTIA ANTIQJlISflMA , t)IVINlTUS INDE ab Adamo Procoplafto humano gcneri concefla, longeq; prxftancifsinia, in quancum nimirum Coelcflia & fublimia ha'C cerrcna & infcriora fu- peranc : Pia^c inquam Divina Aflronomiaab ipfis renfibus oculorum, inilcivagasfiderumvicirsicudincsanimadvercencibus, quanrumadexce- rioraorigincmcrahens,muIcoccmpore indearerumcondicujexcelien^i cirsimorumhominumfacigavic& gcnios& ingenia-.. Tanca nimirum cfl D Ei Opcinii fic ccr maximimajeftas, ucanulhscreacuris ipfjus opcrum fapientia ex- hauririqucau. Cum vcro folusocularis incuicus omnia illa fupramodum admirandi theacri Coeleftis myfteria , mcricacasq; variccaces apparcnces, ca, qiia opus erac fubcilicate 6c accuracionccaperencquirec, excogicaruntommbusfeculis varii Arcificesmedia&orga- na.quibusvifusinpercipiendisSiderumabflrufismocibus juVarccur^, Kincfuncillse co- lumnx, quas Jolephus Judaicarum rcrum fcriptor referc, Adas Nepotes in Syria cxcruxiflc , iisq; fuainvGncamcmoria:caufaad Poflcros infcripfiflo. Huc percinenc^i^gypciorum & aliarumgencium alcifsima; &fumpcuofifsima:Pyramidcsjmuha'q;alia^machinar, a Regi- busanciquifsimis in hunc ufum conflrudse^quales in India,Syria> Arabia,ChaIdaa,^- thiopia, ypgypco,prafercimiflhicinporticu Alexandrino, tumqtioqueahbiincircumja- centibus Regionibus , ubi homincs Sidcrali fcicntia: fedulo intcncidcgebant, olim fpeda- bantUL, Id cnim omnium primum cft, ut in Aflronomicis obfervationcs plurimia: & diutina: idoneis &: errorinon obnoxiis Organis Calitus cipiantur : <\\\x poflca perGco- mccriamcxcogitacisconvenicntibusHypothefibusinquanticatcscontinuas&moturri cir- cularem ac uniform.cm ( quem Cocleflia Naturalitcr, & abfqueintermifsione appetunc atqucexcrcenc) digeruncur; pcr Arithmeticamvero indifcrecas: utadquavis tempora_. conflcnrCoelcflium corporum circuitus &Ioca_,* Intcrcmnes veroqui hacreflrenuc laborarunt,adnosfaIcempervencruncca,quqaTimocharc,Hipparcho,Pcolema?o,Albatc- gnio, Regc Alphonfo, & fupcriori jrvo Copcrnico confignaca funt: quamvis duorum antcccdencium inhis tradicioncsfalccmcxahquali Ptolcmairelationeconflcno: Qui- bus veroOrganis hi indimeciendis SiderumPhapnomcnis pocifsimum ufi fint, cxfchptis eorumutcunque liqnct^. Intcrquarhactriapiacipuainvcnio: RcguIasParaIIaticas,Ar- millasZodiacalcsacquc Torquecum,quodArabibus(uci&: Afbrolabiaplana) pocinsin ufu crat : CcECcra minor is funcmom.cnci, Mulca tamcn fortc alia fucrc , qujc litcris non prodi- ca, adnoshaudpervcnerunc;qua?intantafamq;crebraMundana;fcena£Confufione&mu- tationc, totbeIiis& dcvaflationibus fubindeirrcpentibusfacilc (quod deplorandumcri) inccrircpoteranc?. Rcccntiorcs Quadrantcm,Radium &AnnuIumAfl:ronomiccm-ad- didere,tumquoquequa:dam minonsadhueaftimationisr'. Exquo autcm Sidcrum mo- cusaccuratc noflco .x-vo confideraci ncquaquam ica fccxhibeanc, uciferccalculus ex ullo rum fivc vctcrum , five recentium Arcificum Obfcrvationibus dcrivatus,non immcrito )::( fufpicio- TRAEFATIO flirpicioncmmovcc , media & Inftrumcnta_» quibus inccr obfervandum ufi finc, haud undiquaqiomni vicio caruillo. Quod vcl ipla affixarum Srellarum locaalicer ad niviccm difpolica, quam fcrc Hipparchiana a Pcolcma^o rcccnfica , 6: inde ad nos prop^gaca dcnota- cio, eciamfi cqcerapr^cereancur , facis convincit : adeo uc nc vcceribus quidem , ubi Impcra torcs & Rcges fumpcus cahbus Organis Conficiendis liberaHcer fappcdicarunc, quo e fohda &mecalhca magnificcconficrenc maccria, convenicnciquc amphcudincriccfehabcrenc: ncdum ea , quq Copcrnicus (upcriori ccacc privacis impcnfis paravic : ncc maccrie fohdica- ccnecccjam juftamagnicudineiis,quibusdc(linabuncur,uribus,rufriciGncia,parcimcxopG- re cjusRevolucionumliqucc; parcim cx iis qux adhuc fuperfunt, ilh in ufu habicis Organis quorum unumiParaHacicum nimirum,planc Jigneum, n«c obfervacionibus lacisapcum pencsmcell:, O^ocircacogicanci mihiadmodum follicicemdcab Adolciccncia,an non huicincommdoiubvcniri pollec;varia deinde fucccfsivc conflruicuravihiftrumcnca A ftronomica,dihgcncia & impcndio incrcdibih ; quibus Sidcrum apparcncix cxaitius quam ab Anceccflbribusnoilrisfa & fi<^ dcinceps, doncc ad ulcimum Si incimum_s 'pcrvencum fucric,qui46'p.orcioncs habcbio.Qucmadmodumha:cutcunq;in ipsafigura- tionc repra;fencancuiL.. Rcgula cjus D A habec pinnacidia apud A 5c D vulgari modo paraca cumforaminibus.-liccc mfcnori apud Anonnunquamrimulo: apphcaripofsinrparcllelK; fupcriori, morcnoflro: fjcq; faciliorS^^ exadior ficri coIIimacio.PcrpenGicukim E F G apo- fleriori parceappcndicur,uc cjus bcncficio cognofcacur.quado Quadrans riccdifpoficus cfl; ica ucinfcnuscjuslacus A B Honzoncisarquihbrium ,alrerumvcr6 A Cvcrciccm capitum cxadcrcfpiciac:cocumq;QiiadrancispianumplanoCircuIiaIicnjusvercica]Jscongruac. U auccmQuadransicariccdingarur,ficpartimpcrcochIeas,quashabec juxramfcriorcdiipo- ficioncm Pcdcftalis,Iircris S.norara$,parrim percochJcamad O M, quaripfum Quadranccn 0II1C& dcprimic,donec pcrpcndiculum monflrec,ipfum conTcnienrer eflc ordinacum Jn fiflicenimispedcflaliNMOPC)RST,quodcocucumca:rcrisrcquificiscpurocflferro,ub 'a poflcriori parcc juxca H illi aftigirur,Eflc]; propc N nonnihil mobilc hoc fulcrij;ica uc Qu:i drans furfum acqus dcorfum rrodi queac pcr cochl cam O M. Nam Rcgule fcrrc M N &0 N pofllmcarcbari&iamphariincermcdiancecadccochlea OM: ficq; quadrans una parumpci accolli vcl dcprimi prouc opus facrir.Circumducicur crjam is in concavo canali N P,in qua- cunc]; Coeli plagam lubucric : hrma camcn mancncc cotainfcriori pedcfl:alis parcc;quam li tcrx RSQT flgnanc: qui^ infcrior portio ca,qua vidcs forma fulcmiina prebcc,uc Qu^adranb firmiccr confifb c in f uis quacuor cochlcis per liccras ST indicaris : quas cochlca: (uci dixi)co- rum Infl:rumcncumindcbicumfirum dirigunc. Innicuncur auccmhx cochlca? Jaminuli' fcrreis f Ljbfliracis juxca T: quibws quicfccntibus in mensa quadani V X Y Z cochle^ pro lubi cu circumgyrancur... Acq; h^cdcQu^adranceejusq;pcdcflali gcncraliccrindicacafunco. Qux aucenialiquaccnus viflcur incra Ccncrum &c minimum QuadranccmpicturaLK circulari forma comprchcnsa;ornarus caufa cum quoq; uc fliu Hicroglyphica fignificacionc quidpiam doceac,cxfculpca cfl;cum alias fpatium id forcc vacuum Jn qua figuracionc (uc &: hocobirer indicem) adarborcmalceraparceviridcm &frondofamJuvcnis laurcainfigni- cusjin quadraco faxo fcdec, & una manu Globum Coeleflcm tcncc,alccra librum in viridi ec- |j am graminc; & herbis radicem arboris obregencibus pcdcs cxtcndcnsr', Ab aha,lcva vidcli- cccArborisparccradix cmarcidaefl:, &:frondesfl-crilcs, foliisq;carcntcs: incerqua^menfu cxifl:ic,habens e flngulis fcrroaliquid ; qua^ in hac rcrrcflri fccna a morcalibus in prccio ha- bcncur;quahafunc:cifl:ulanumisrcfcrc4, Scepcra,Coronq,Armagcncilicia, Torquesaurei, Gemmx,Mundusmuhebris,Pocula,Charcar,Tcflera:,acq;hisfimilia: quacomniafcclecon_. quoddam,mortcm rcprqfencans,manib,pcdibusq; circumdac,quaficaadfcrapiac. Supra lcripcum vcrocft coci figura; hcmiflichium ,quod fcnfum Allcgoricum explanac : riviMus /NGENio C0ETERA//0RTIS £runt :icaurprior pars hemiflichiiadcxcera & viridiaiboris parcc ubi juvenis ille Philofophans fedec,canquam in fchcda fcripca c ramis depcndcac,alcc- ra, fequens hcmifli chii porcio. Qu^ibus innucre voluimus folidam dodrinam , pracfcrcim rcrumCoelcftiumfublimcm cognicioncm, vicar&mcmoria^pcrpccuicaccm inhifcc ccrris largiri : Rcliqua omniafrivola&caducacflc; acque unacum hominiscorporc intcriro^ Q£andovcr6a:ccrmcaccmRegniCaclorumrcfpicimus,cunchiecipfa,qucEnuncaviridiar- boris parce func, in poflcriorem rranfeunc : fiquidcm finici & infinici nuUa derur proporcio, Tuncq;aliccrmucacurhcmiftichiuminfcripcum, nimirumfic:riviMus /n Christo,Coe- TERAcJWoRTis£RUNT;icaucpriorparsarboriviridi,alceraftcriliadapcccuii,. Incraviridcm auccmarboris facicnij» Chrifhvitce & do6trinac Hicroglyphicaquacdamindicatioeft, Cx- ccramancnc,ucancea:nifiquoddo6trina:&invcncioncshumana:ccjaminl'a:vam&poftc- A riorcm. EXPLICATIO FABRICAE eT VSFS, TiorcmarboriSjdcrilcmniniirumparcem verganc. Quibus innuimus, nihil homincmbra rc,& mimorraiicatc nia-ccrnumdonarcpoHc, pra-ccrmcricumfihi Dei Clinifli rcdcmpro- ris, ejusq-, Dodnmr 5c Vitx obrervanciam_^, Qua: fHigula hic,liccc fortc citra rcm, ob pidiv ram adjun^am cxponerc lubuio, Ab alccra Quadrancis parcc Canon ziphns cxcifus cfl, qm minimo negocio oilendic,quid iingula punfta Nonniana: (de qua dixODivifionis m Alcitu- dmibus qua^ficis cxhibcanc. U s u s hujus Quadranus cll;in capicndis flcllarum 5c Luminaritim Alcitudinibus^quanJ do non fumma rcquiriLurpra;cirio,icaucmcra duo vel cria minutahanc rcircrufPiciac, Diti-J eac uriraqicuncplanum Qiiadrancis vcrrusfidusobrcrvandumSc rirc difponatur pcr fuasj cochleas,uci priusditlum,doncc pcrpcndiculummonflrccomniantcconflaro. TollaJ .urq; cunc, vcl dcprimacur Regula AD,donec fiduspcr foraminaauc rimulas diopci-ariun ccrnatur,auciumenSolismtromiccacuradamufsinij.Sicq', firmccurab alceraparcejuxcaD,| ubicochleolamhiclaccnccmhabcc. Monftrabiccnimficincxccriorclimbo,ubidivifioncS| fuhc vuigarcs, excrcmaccjam Regulac pars Alncudincm qua:ficam inrraquina minuca;qiio-j rumquoqucdimidiamvelccrciamparccmaccuraco intuicuaflcquiliccc. AcfiNonnianJ {Iniu: divifione ucilubucric,vidcndum efl:, ubi Rcgula aliquod pundum in ca, ubicunquc tanicm,cranfcac5&numcrandum,quotumfuilludpundum, acquoccaliaillcQuadrans concincc:cumquibusduobusinTabulam ab altcra Quadrantis parcc exfculpcam Jarcra- litcr incrandum, ficque in arca juxca.. communcm concurfum invcniunrur Gradus^ Minuca, Alcicudinemmenfuracam pandcncia_..Idcm abfqucTabuIa perRcgulampropor- tionum, nonmulcoIaborc,cflricicur: poncndoprimoloco coralcmdivifioncmcjusQua^ drantis,inquo punO:um aliquodipfaRcgulacontingicun.. SccundoIocoGraduspo, Tcrcionumerum ejufdem puniflia principio , eoufqueubiRcguIacfl: fic- quc quarcus perada opcracionc folica oftendcc qua:ficum_.. Vc- rum hqc Nonniana racio non cfl fufficicns in praximc- quc habec in rcccflu quod in acccfrupollicc- cur j uci cxpcriunci patcbic». QVA^ aVADRANS MEDIOCSIS ORICHALCICU^ A2IMUTHALIS. tA 3 EXPLl- .^ EXPLICATIO FATIRICAE ET P'SVS, fllc Quadrans ABCexfolidaconOansIaminaOrichaIcica,habecaccntroad ; lcircumfei^ntiarn A B pauloplus feiquiakcro cubico.Crafsities cjusefLfenriC |jlcniis]aticudinisdigitiXontinecverointracircumferenci?.irj,nonfoJurDdi- ^^0 pvifionemnobisufitacam perhneasScpunda rranfvcrfaIia(dequaalias)Scd& |^3LI!l^onmanam iilamClarifsHni MatlTfernacici Hifpani,inhbelloeruditodeCrc- pufcuiisprodicam. cujus in pnori memini,alia ramcn & magisaccomodara- tioncampliacam, ica uc plures contincat fubdivifioncs , corum pra*lcrcim numcrorum oui in aliquocas integras partes diftribui commodc poifuno. Qua i n parte Nonniana invencio nonparvamxlifficultacem ingcrcbac ; cum etjam pcr/e nonfit lufHciens omnibustotius Quadrantisminutiis, ncdumuthorumerjam. fcrupula{ccunda,proutillevoluit,mamfe- flec.Jdenimpotiusincalculo,quam praxi locum habec : uci aliasfkpc fic falli Tyronesin_> hac Arteufu venio.Additurctiam Tabul;i inalrcra Quadrantisfupcrliciecxci(a,qu^ Divi- fionesiIlufi:rar,&:fincultcrioreca]cuiouf;bnsficiIIim'a;aptasreddit, RegulaejusDE tota Clialybea eft,uce6 promptiLYs dired>a icmper manear.A t fimul inaurata, nerubigine inficia- iur_ DuodioptracircaDEhabetOnchalcicajubiinfcriusE rimuias prionpinnacidioadD parallclasicui oculus obfcrvacoris app]icandus,exhibct;quo fidera undiquaq; circa primum pinnacidium cocollimatius&ccntralitcrahlq; cmnihallucinationecollincareiiccac.Qui modusnobisinomnibusfcimeInflrumentisufitatuscliJflq;ipfaReguladataopcraQua- drantis radio longior tacla apud A K ; partim utcii ca infcriorcm fincm ad Eintercolliman- dum digitisfacileattollidcprimiq;poisir,donccAflriobicrvandicxquifitapateata]titudo, unaq; Azimurhunij.Qiia? etjam ubiq;, prout mota fucrit , flrma maneac:alia ab alcera QCia- drantisparcccircaDpluma( uti vocant) tcnui Chalibca eamficcontincnte& oblervanr^-: iiceoexadior&commodiorfiacobfcrvacio. EveniccnimfermeficacfiQuadrans in radio haberec longicudinem, qualis efl DE : & infupcr, ne inferiora obftcncfulcra,aptiortfl: cra- ftacio, AcquehaxdcipfoQuadranccfaciscxplanarafunto. Fulcravcr6,dequibusloquor, fic habenc : Primum volvicur ipfe Quadrans , cuidam ccreci oblongo robufto ferroafhxus, circa H pcr cochlcolam : ica uc aufcrri pofsicquando 1 uber,in quodam canali , qui cxterius eashabetangulum,qua:apparcnt,circum.gyrarionesfrmirudinis&ofnatUscaufa_^. Cana- lisaurcmipieinfenusgcflatalii:miTgu]a,*"quiijuxtaK6,diip6ficio,cacceraq;huc conduccnriadilucidcofl:cnduncuc_, E6icaq;lcclorcmharumrcrumcupidumremicco:nbi crjamplurainvcn!trharrcMa'chanicam,camhujus,quamaIiorurnInflruiiicncorLrmracio- jnemconccrnencia:quxomnahicannocarclocusnonpacicbacuL.Ecqua;ibicircadivifio- Inis & pinnacidiorum flacioncm prolaca func, ih omnibusaliis Inftrumencis, quibus hxc ac 'commodarcoporccc,incclli^ivolo:necamhicquam alibicafafiidioscrcvoGarcopus fiu. Ild lakcmrampropcerhocqtiamcxccra rnftrumencahiCmonebo, oporccrc ca-.omnic}c ^iarcecflcquamabfblucifsima-,, Idcoq;idoncos ArcificcsMcechanicosadhibcndos,quicali laffabrcclaborarenorincaucdifcanc.Ecfiprimavicercmcmncmaca (uciajun >' ^ '\- iccrmc,ha«dpigcacfl:ru£lorcmdenu6rcicerarcopus,caq:omnimodecmcndarc,quardcfi- JdcrancurrdonecnulliVicioobnoxiafmc.Qucdipfaobfervacioincclligenrifacisprodic, va- Ifficadminiflraca-., Hincfafic,ucpIurescommodccxcipiac. Habccnihilominusduorumcirciccrdigicorum |Jaticudiiicm;5i fingulis minucis cxprimendii cranivcrfaliccr ( uc dixi )c.?pax cfi.Quadratum jvero, quodinarca Qu^adrancis A D E F conipicicur,unaq;huicdccurii\rim incidenccsco- fgnationesfulcriialccmloco&majorisiirmiiaciscidcmadapcancur: nifiquodQuadratum iUud ufuiquoquecflcpofiic in dimcnfionibus Gcomctricis quoad alcitudincm & lacitu- dincm rcrum , qux in terra confpiciuniur , arqucj in ea hommum luborc cxcrudlas funt-» : Qucmadmodum alias Inflrumcntum illud , quod Quadratum Geomcci icum ap- ipcllavicPcurbachius; hxc& fimiliapromic : vclurii.bcodemcximioviropccuIiarilibcUo cxplanacum & dcmonilracum cfi: : acqucaliiis id ab lis, qui Ailrolabhms cxplicanc, praier- cini quoadcjus (ucivocanc) dcrfum,minorincgociolicccnonadc6cxacI-e)!ndicacur-^.Al- ccra adapcacio,qux circa ha:c di(fl:a ccrnicur,acquc a poflcriori Quadrancis parcc incciligcn da venicjformani litcvq Y repra:fcncans,acquc his cnbus liceris FFX Y confignaca^propcercsl •dcxL,ucipfumQUidrantispIanumHori2onci, cuiinvolvitur,adangu]umrcdlum,quomo- docunq;circumgyrccur,fin:ac;unaq:caparrc,quaHorizoncijuxcaY coniUngicur, cochlco- laquadani,ubiopuscfi:, icafigar, ucin iuolocoibiimmotuspcimancns.Gradus Azinuuha lcs commodcdcmonitrcc.Ubi ctjam RcguIaqua^damaCencro L vcriuscochlcam Ydu£lal conjun:;ic iulcrl cxcreniicarcm cum inferiori 6^ media Quadrancis partc, quo co firmius o-' mniacohaTC.aat,&:pariccreircumagacur: plumcola ccjaminfcriusadcochleamaddica , u confidacQindransinquovisloco abfqucomnivacillacioneimmotusr** Quodvcro Qna drans hicnon cocafuafuperficicibUdus fic, feddifcriminaca, quadnlaccra I1tplunmum_., qiiaMnco vifuacur,habeac,idpra:betucilicacis , quodminorisficpondcris,arquc obidnon faiccmfi.iciIiLiS cra^tari, Ccd. ccjam ab uno in alinm iocum , (cujus crjam causacxpartibus c6 {lac}cransfcrnqucac:uc pbftcaplcniusindic^bimus^^.DcrcgUlaquoq; cjusdiopcrasgcftan- ccjjammoxdiccmus ubipriusdsHorizonrcAzimuthalinonnuIlacxpIanaVcrmius: f qui- dcmdiopcrjeiila^oblcrvacioni tam Alcicudinum quum Azimuthorum paritcr infcrvianc. Ideoq;RcguIaipfafuoplanoobIongiori&:Iaciori , planoetjam QLiadrancis ubiq; adjacet: adcouccjaminfcrioriiuaparcc, A Squa promincc.candcm planicicmcxadcrcibiciac.&di- opcrarcumfuispinnacidiis huicccquidificnc, tumquoq; Orihoeonalitcr infiilanc: aliasc nim Azimuchorum(ucde Alcicudinibus nondicam)accurataficri ncquircc pcricrutatio» Hori2on aucem Azimuihalis (dc quo dixi ) infra Quadranccm cxiftcns , adcoquc ipfimi fu- Acntans, pcrG Hl KexprimiLurjhabensinfedecuflatimadanguIosrc^flosfulcmina.uteo firmiorpermaneac,atquecircahorum angulos communcs, inccncro nimirumcjufdGni-j HorizoncaliscircuIiQnadrans tocaliccrinadapcacaillhiccanalircvolvatur, Habccinfupcr juxcacxcrcmicaces carundcm concignacionum quacuor cochleas M N OP, quibus rotuj;, horizon,adeoq;ipfcQuadransiIIiinfiiTcns,icadiriganrur, urhicpIanumCirculi vcrcicalij cujufvis adamuGim imicetUr: IIIc vcrnarquilibrium Horizoncis: quoucriufqucufustam quoad Alcicudincs quam Azimujharircconfcrc. Rcgula (cujusnonnihil anccamcmdni) ipfi Quadranti applicaca S V Tcodcm moado fchabec,quodfuadiopcra & pinnacidia,qur* admodumin prioriindicacum cll:, nifiquodinfcrius juxtadiopcram S habcacdiiasanias, quibuscommodcmanuaccolli & dcprimiqucac,proucAltitudoobrcrvandarcquJi-ic :tum quoquc,ucfuopondercalccram Regu!a:parccmT A quafiin arquiljbriodccincar» Carcc- runi mfiftic cocum InflTumcncum lapidi Qiiadraco aliquaccnus in larcribus excavaco,com- modiorisufusgratia,qui perliteram Q^cxprimicut-, Is vcrocolumnrclapideci: K firirdccr innicitur,uci ipfaiiguraha-cfticisoAcndic.HabcchicQuadranspraranccccdcntiinfuafabri- ca id commoditatis.quod cani is quam Horizon cui infiflic , omnir.q; rcliqua huc pcrcincn- tiafaciledi.sjungiacq;iccrum intcr fc compOni qucancquoabunolocoinaliemporcacioni, convcnicnci chccaidoneusfic,cum ctJAmnoncocconflccparcibusacque prior,&ha:coch- lcoiishincmdcdifpofitis nonfalccmdisjundioncnl, fcd& facilc p:\riccr, ucanceacompofi- tionem admiccant candem. planc quam prius : Idcoq; hunc Quadranccm Azimuthalem,ap- pcllarefbleoporcaciicirLj» A 4 Usus EXPLICATIO FABRIC obicrvscio in rJi- ouotaminunpartcrequiricur^ nonnmiium cOclidcndum : qualcsruncillar, quicSoIariSj curricuhrcftiiutioniinicrviunc,ubircscircaminiraavcrfacur,acqucrcxti^,vcladminimuiri rcrciaj narcis umusnhnuci prsccihoncm rcquiric; quam cam parva Inftrumcnra , qux unum' velicrqiualcerumcubicum compIcMMJ.Wh*Mi>iHiBP'a«!»aKMjjm.«imiui'iLMW!wi^^ EXFLl EXPLlCATiO FA^BRICAE ET FSFS. •>«fN^.*^rium,quam jcxtcrorum fidcrum errancium & inerrannu cxaxile incra tcrtiam vel quarVani minut! par- jtcmdimccicndis;mod6fexcim Cofli parccmnohcxuperarinc. Qum&jiicfirmacoalicer Quadrancc, ita vidcliccc uc A C Zenich rcfpiciac . rcliqua pars haberi pocrC A t fola- Ai ciru- dincsficdcprehcnduntur.nonaucemfimulAzimuLha.,, Talisfcxcansrtdmbdumaccom- modus cfl non rolummodo Alticudinibus,fed & Diflantiis flellarum ad amufsim rim.andis. ncquc difHcuItatem aut incertitudincm aliquam in hac pragmaceia iu§[gcric, cum pau-- cisconn:ecparcibus,iifdcmq;(ucidixi; inccr fe firmicer contignatis; nc^inccr obfcrvan- dumcxcra dcbicum ccnorcm quidpiam in co diflrahacur : unaquc id prarflacCouod 5c anceainnuimus)ucintliaccjamlocanondifHcuIrcr,&abfquel'afioncacqucincommodo cranfporcari qucac. Qu^odin quibufdamInfirumenci$,quacenLi$lienpoccflpra'flan- dumvcnic: nefervi locorumfimusr^.Oporcccenim Aflronomumpotius,qu4m alius Philofbphia: partibus dcditum Korf^oTTcArTKv cflc,& ubiquclo*. corum^proucfert commoditas vel ncccfsicaiiiiaia rcputarc Patnaui>, aVADRANS xMVRALI SIVE TICKONICUS. EXPLI- «»■ EXPLICATIO FABRICAE eT FSVS. Uatraktem maximum pcr B D E C hic rcpra^rcntatUm Muralcm ilvc Ticho- nicumjamurocuiinfigcbacurdidum,etjamconficricuravimus,eiblidoOrichal- cofufum&apprimelevigacum quinqucdigicorum in laticudinc, crafsicudine^- auorum,quiqueinrua Circumferenciacantxcftcapacicacis, quantamradiusleu Circuliicmidiamecerpene ^.cubicorum pofluIatL». Icaquc Gradushabecadmodumam- plos,ade6 ucfinguIainhisMinuca_.adhucinrexporciunculasfubdividancuii..Ideoq;,dena qu2;libeclcrupulafccundadifcriminacim|exhibec:ade6ucfemishorum,quinavidelicecfe- cundainhisnondifliculcerdifccrnancur; Eaq; omniaperpundla qua:damcranfvcrfalia_., fubcilifsime,modo nobis uficaco fignata..» AfKgicurhic Quadrans murocuidam MP Q^cxadifsime Mcridicm fuo planorcfpi- cienci : Idq; firmifsimis cochlcis , ut nulla vi auc robore a fuo debico ficu , qui prxordinatus ed, uc Quadranci MeridianiCoelcflis ab HorizonceinZenith duclo,ab oppofica camenpar- ccapprimcficanalogusr'^ Habccinalccromuro LMNB, quiprioriOrchogonaliscfl,&:0- riencem acqueOccafumad amufsimrefpicic,fuperius, ubi Cencrumeft Quadrancis , Cylin- drum quendam Onchalcicum inauracum,nc aeris injuriis fic obnoxius , auc quidpiam con- crahacmquinamenti,quicxhibccurjuxcaliceram A inforaminequodamQuadracOjejufde muri, quodcxceriusapcnri& claudiconvcnicnci janicula poceft,uccirca_jCylindrumdi- ctum fiac hinc inde collimatio cum fudum fucrir ; idq; per pinnacidia five D five E* Duo c- nimhabethicQuadrans, ucquocunquclubuericjuciliccac: proucAlcicudmimenfurand;^ magisoporcunumfueric» EcqUodlibec eorum Quadracumin plano ad magnicudinerrL» unius palmse : Cui ccjam Cylindcr ance didus fua diamecro omnin6 corrcfpondec,ica uc pcr rimulas parallelas ipfis pinnacidiis applicatas fiar inomnibus quatuorlociscoUimatio ; fi & alcitudo & tranfitus per iMeridianum fimul capienda funt : Alias fi fola dcfiderarur Altitu- do, per fuperiorem 5c inferiorem rimulam,fimilesq; Cylindri partes,Obfervator , qui juxta F appingitur^negotium abfolvir, & numcratam al titudincm al teri n:udiofo,qui juxta G me- ffarcumIucernaafsidet,IibroObfervacionuminfcribcndamindicat,lJcver6cempusObfer jvacionisacqueipfifsimum momencumcranficus perMeridianumunaconil:cc;Terrius qui- jdam apud H notatus Horologiis I & K atcendic, quando Obfcrvacor apud FfignCi dac,quod eciamtemporismomcQCumaDeo,quijuxcaGfedec,libroinfcribicuii,. Horologiaaucem, jdequibiLsdixi,caliafunt, utnonfolumfinguIaHorarumminuta,fed&fcrupuIaearundcm •fecunda, quaficripotelijpra^cifioneindicenc, &a'quaIitatemrevolutionisCoeIefI:is«mu- llentun., (^od licec difticulcer pra^fiecurjtamcn adhibira reqiiifica diligencia_. quodam- .modoobcineripocefi:,,&virium,fiquodobrepferir,animadvcrci&corrigi. Ideoq;duoad minimimi efle oporccc horologia ejufccmodi,qu6 unum alcerum emcndcc,llcubi opus fuc- !ric.Nosquacuorejufccmcdi inpromptu habemus,quortimunum &maximumcribusro-. itis rem oinncmexpedic, quarum majorcfohdo& puro Orichalcofufai20o.habccdenticu- lo5.Eftcniniindiametroduorumcubitorum_r,Cieterahinc?ifI:imctuc-.,Reliquatnahoro. Iogiaminorafunc,&pIuribLisindigentrorulis:horumver6omniumcompofitionemaIias V, D. Dabimus^* Quitcunquc incra Quadrancis circumferenciam cernuncurpidurje,Dr- nacusfolummodograciaaddica:funr, &nefpacium incercepcum otiosevacarec: qtias etja brevibu,selucidarc,licecminusadrcmfaciac,noneritufq;adcoinconveniens.Infraliteram TappidaertmeicfHgicSjfellqad mcnfampofitaeafsidentis in longa talarivcflenonnihil fe- fe reclinando,itaucdexrcram manum verfus Cylindrum,indicanti fimilem porrigac,alcera mcnfc juxcalibrum& qua^damaliaimponac, quafificindicarcmmcisfi:udiofis,quidob- fcrvandum fit;&: quomodoinufum idredigendum_».Hanceffigiem magnafolerciacxprcf- fic Thobias Gemperlinuseximiusarcifex(qucm mecum AuguftaVindelicoruminDaniam olimrcceperam)idq;camcompecenter,ucvixfimiliordsripofsic.Eftauccfccundumflacu- ram & magnicudinc totius corporis equali forma rcpra:fentaca.Supra capuc juxca X Globus quidaOnchaIcicusinauracuseffbrmacur,quirociihsinceriusfoIertcradapcacisfp6cercvol- vicur,motumq; diurnum a:mulatur,& & una Solis atq^Lunze cxhibec concraria_. curricula c PoIisEcliptica:: adeouceciam Lunafeiinafccundum faces &illuminacioncsfuas,cas auge- do vel minucndo,convcrrac,Sol autem incra z^.Circulos horarios pra;cer mocum propriu circa Axes/Equacons curfu diurno revolutus,fingulas diei horas una^ mon{lrat,tum quoq; ccmpus ortus & occafiis fui, atq; per meridianum utrinq; tranfitus. Hocartificiofum «uto- uiJtflova mc ipfo ad invcntu, & meis fumptibus con{iru£lum,anno Domini i^^o.Sercnifsimo tPrincipi,DominoCHRisTiANOtuncRegiElcdo,Dominomeo Clementifsimo,cumantc B annog E XPLIQATJO FABRICAE ST VsVs. anno3 nimiinl ^xirca a-raris VTi o fua' anniim I4.me iii Inftila Venufia Uraniburgijadhibiris,; {ecnm pnvtervcliqtjam NobiliraremAuIicam,tnb'JsRcgni Scnaronbus primanis,qui runc' gubcrnacioniprt^tacrunc,cIcmenrcrinvilercnoneftdcdignacas,fubmirsedonoclcdi;quod eciamnumconfcrvac. Seremfsimusautem Rex Ele^lus, mcviciisim corquea-area, pcculiari^ arcificio, qualemgcfiarc runc folcbar, piiIchrccJaborara& fliacfhgiedccorataclcir.cnter_.' donavit.Supra ipIumGIobum,dc quo luinc diximus apud Jircram V Bibliothcca^ noflra: a-' liqua parsrcpra'fcncarur_. Ad Y ver6& Z appendenr binaeiligics inna rocundum ambita folidc cfrbrinata;, quarum una_. eft fcrcn iftimi & pocentifsimi illius Regis Danorum Fridc- rici 1 1 Jaudstifsima memoria: : altcra lcrenifsima- Rcgina^ Sophi.^' , cjus Conjag!s Illiiilrifsi-. mo:, qui me meaq; iludia Rcgio &: clcmenti favorefempcr profccuti (iinc. Porro qugj in iii-. ceriorepiin medio Muliei rotundi conll:itutam,GJobusiJIe maxmiusOrichalcicus^* pe- dum in Diametro,qucmpofJ:ea fuo loco cxhibebimusScdeclarabinuisr^. Tandem inha h(jc omnia juxta numeros 9. 10. 11. fpcdatur Jaboratorium mcum Chymicum , quod totam fub- ; terrancum&crypticum erat: in quo i6.varii generis & fornia^ adornaram fornaccs ly ronomicasr'. Nam&huicftudioimpense,abineunteetiama:tate,non minusquam A(ho- nomico addiclus fuij magnaq; diligentia. ncc parvis fumptibus idcxcoJui, UJtimo juxta pe- desmeosapudnumerumi2.recumbicCanisquidamcnoflrisvenaticus, quiadmodum fi- dus & figa>c erac.Isq; incaforma& quancitate dcpidus, qua cerncbatur : non tam Ncbilita- tis,quam fjgacitacis&fideJitatishierogJyphicunxj. Sicq; piduramuniverfam, quatcnusii. tam parvafcrmaimicari eam Jicuic,breviccr cxpoficam habes :quam tres divcrfi & excelie- tcs Artificesmihidepinxerunt.Effigiemmcam Augun:anusiJJe,dequodixi,pitlor, Archi- ceifionica ifl:a,&qua:hiscomprehcnduiitur , Architedusmcusjohanncsde EmbdaSten- vvicheJcffinxic.QuafverofupraiIJainftardelcripcionisRcgionum& montium,ubictjam_- Sol occidercvifitur,depidafunc, Johannes de Ancverpiapiiflor RcgiusCorona.burgc:ifis appofp.ic. QuiJibet cnim cx dictis tribus artificibus in hoc ipfo, qycd fcccrat, prae cqtcris cx- cciluit. Demum fupcrius juxta R S efl efTIgiei & totius pictura; infcriptio,.prout vidcs^. Usus hujusmaximiQuadrantisefVinrimandis accuratifsinicSiderum fubliniirati- busintrafextam uniusminutipartcm,coJIimationefada per aliquodpinnacidiorumcri- mula fuperiore &: infcriore juxta Cylindri utranq; ct jam circumfcrentiam hifce anaJogan^: &:numerandoipfam Altitudinemin fuperficie Quadrantis extcriorcapudpofitumcjufdc pinnacidii.Poceftctiam momcncum tranfitus pcr Meridianum una ab utroque Jatcrc, cam pinnacidiorum quani Cylindri habcri inrermediantibus horologiis accuratis,de quibus di- xinius. Quomodo vero ex daca Altitudine & momcnco temporis , quo fidus Meridianum tranfit,adhibito motu SoJis, ejus locus conflec, Aftronomis notum eft.Confirus fam pJuri- mum huicquadranci inrcftitucndomotuSoJiscxejus AltitudinibusMeridianis, 111- tromifla CyJindri umbra quadrata in intcriorcm partcm aJicujus epinnacidiis inquadrataetjam figura umbram illamad amufsimexcipicntcSc comprehendence. Adhibui nihilominus& aliosmagnos Quadrantcs in confihum , ut rcs tam fubcilis omni crroris fufpicion© vacarcu« QVA- „^itimimmtim^kitUmim QVADRANS VOLVBILIS AZIMUTHALIS. * n * lEtftl- EXPLICAT/0 FA^BRICAE ET FSVS. i S!i?Sv^'^ A D R ANTFMVoIubilem,qinnon folum AIrirudinc$(utiScxransanccdi?riusaut^m,ubijuxtaGeadcmcolumn3- iii I ofuiidunipcumcn cxChalybc dcfinic, ac in pravo foraminc pancer acuminato rcvolvi 'tui;idq;in laminulaquadamCha ybca; qua:quatuor cxtra pofitisCochleoIisquaquAvcr jlimopusfucrit, trudipotcl, donccQuadrantnsutraqucpcrpcndicuIacirca A incipicnti?-.' t< iu-.raS defincntia tam plr.num Quadrantis, quam dorfum cjus, quomodocunq; cir^um-| i^;vrarur, iradirig:\nt, urcxaclecirculumqucmvis verticalcm rcpraientare d^pranendaiuj i iOa'')d cum frmel fAclumcfi:, & circumipeclc in varias acdiverias Mundi plagas Qindrantis # diiooficioivbus fic:u'rprovifum,ntqueCochlcisrcquifirisfijmatum,nonopr.seritmu!ro 'teninoicpcrpcndicuh$attenderc,anvide!icctQuadranse fuarcquifiradilpofitioncdimo- tiisfjc. Ncn;enimidcontingcrcpotcn:, nifimagnaaliqua violcnria cx improviibfupcrvc- inicntc:iumq;modor.nccdidofacilcrcil:ituipote(\. Adcocnim firmitcr iaxorotundo H> 'q:iod ilihdum cxificns profundc in tcrraalio fundamcnto lapidco immotuni infift.t: 5<: fcr- r.uTscJuunr cij.m\quc)ddecui]acim iupcriuscxtac, dcquodiximuro Aabih innicfns,ncn pa tiru» columnamforrcam, cui Quadiansaffigitur,clliofaraminc, quod innicdioc{l,quid- piam vacillarcj. i Mu Rus jiurcm isrotunduscirculipcriphcriam C^a^fl-c cxhibcns(cu'usdiamcrcr cfV r^circitcrcubitorum, quoficfufhcxns fpacium fit intcr circumfcrcnciafn Quadranris &: concavitaccm crypca-jquoObrcrvacorcommodccircumircqUcat) habeciupracirculum.- Iqucndam M\cchinica,limini>Orich.ilcicisven:irum,mqtio omn a roriusHorizontis, Ccui luoequi'ibriocorrc(p6dcnt)Azimuthaminutiasfubdixifaprebct:unaq;immotu.^pcrfiftir Ixordiu Azimuthorum,quodaIincamcridicidcpcndcc,ranra circiifpc(ftionc & (ijbrilitatc inquifiru urnullominutoObfcrvatorcmcIudat.Meridicilinca nlia,6iIongcccrtiorcratio^ nc, quam hadenusaquoquafadum nobis cx ipfa AcIlapo!ifri,qUandopra(trtim. urrir.q' a polomaximum Angulu rcmorionis Horizontaliscauilatur; atq: tuncqn. fi incodcm Azi-^ muthipunftcaliquantiilumfubfiftcrc vidctur,adinvcnfarationc infalLbili &: cxpcdica..» Ouod&opcraprcriumcrac;fiquidcmp«iucainObfcrvationibusAfl:ronomicis citralincq Mcridiei accuracHsimam cognicioncm pcrficcrc liccat. Trad^andi 5v cbfcrvandi ratio iru hoclnrtrumcnrotaliscfl:, utmquodcunqucfidu$Coclitusdcnofandum,dirigatur;circum- volvcndo planum Quadrantis ; & attollcndo dcprimcdoq; cjusrcgulimi cum fuis dioptris, .donccper rimulaspinnacidii juxtaoculumcxificntisprimum tfupcriorcfidus illudinfu- pcriorict'amCylindnIimbocxa£lcconfpiciatur:atqucidcmparitcr mox fiatpcr infcrio- ,rcmrimulam,inferiorieciamIimboattcndcnti, SiccnimRcgula, ubidivifionesabfcindic juxra K, al ticudincm A flri qua-fi tam cxadifsime parcfaciat, Si vcro cadem opcra Azimuthij quoquclcireanimuseft^volvarurparumpcrhincindcQuadranspcrfuamcolumnam, do- ,nccidcm fiduspcrutranq;rimu!amlatcralcm juxtaplaniticm utriusq; latcris Cylindn fi- imuIconfpiciatur_-«TunccnimindcxQj^ncircumfercntiahorizontali unaipfifsim.umpan ^dit .A/imurhurrL». Quoniamvcro hacduoobCoelicontinuum& vclocem motum , non ifacilcfimul & fcmcIdifccrnuntur,prcTfi-ttfigcrcindicem QJ^nccrtoaliquo Azimutho, cui jfidus appropinqua;c cxpcdando doncc, co motu univcrfali dcvolvacur,atque in codcm m flanci EXPLICiATlO TtA^BRICtAE ET FSVS. ftanci aIcitudincmmotarurrumvcldcorrumRcguIqdiopcracapicndo:QuodnulIofcrcn£ gocio ?.dminirtraCLiE>« UsilshujusOrgani cft, uciali6rum,qu:^pcr Alticudincs^ Azirnurha cxDcdiurcuii.. Habcccamcnpra-aliishanc pra:rogacivam, quodcitralaborcmomHJapcr ipfunicxa QjLiadrantcfatis pnrci- ■scidnuodquarritur,ucQuadracofuIciminis ,&:commodioris conVOlucionisgtariiicurrLi comDrc!ie!idence, etiamfi nulluscjusalids foret ufusr'. Airamen 6. hoc in iplb Ch.^.Iybe quam fijbnlifsimedivifumefl, noftra quoquepcculiariranonc,ita Ucquodlibcccjuslacc- lum, qu?: circumfcrcnciam Q^iadrarttis ambiuaCjCamquodHorizonccm Y) C quamZe- nith R C rcfpicic, canonii finuum ultimum numerum 6. Ziphrarum comprchendat; &rc- l^ula a cent ro per totum planum duifla , tam in Quadrantc quam Quadrato ahitudincm pe- intam incerobfervandum demonflrcc: iAhic pcr Graduumffqualicatcm; hic vero fccun^ !damfinuum&: Triangulorum racionemCcometricam, &:nihiIominusres utrobiq; inti- jnum^ idemrcdit, PcrQuadrantemverointeiligitur A G Ai E,Per Qiiadracum A BCD^ jPcrF.eguIam APQ^, quar ctjampinnaciditum&dioptraapud P. habcc,cum quoqucCylin- lclrtimjuxcaccacrum A, Fademirationcproutinprioribus. Potedetjam parsRegulae P Q^ jqua: 0^adranrcm-CXcedit,in tantum , ut CUTadrari Angulumaccntro rcmotifsimum attin- i(=;at,aQlii vcladmii. proutlubucrit. Porrohabctbocrnftrumentumfuaquoquc fullentacu- lia ac conrignationcsfulcri & rtabilicacis loco , pauciora ramcnquum antcccQcns, fiquidcm totum fit mctallicum , ^c nc nimum horum pondcrc aggravctur, cum &ipfit cuafi cofla: 'per literasG H NO, li EK LM, dccuriatim fc tranfeuntcs cfolidoconfVcncChaIibc,cotum- queQnadracumunacum comprchcnfo Quadrantc infuoplano& jufladifpofitionc» fir 'miccrcontincanc, Quin^chicQuadransUnacumfuo Quadratocolumma; fcrrearadmo 'dumrobuftasjuxta X & Y affigitiir, cuniquactiam commodc& facillime in omncsCccii fparccs convoIvi:uiL,, Gyratur enim columna illafjpcriu.-;in rotundo foraminG, quod:n-i 'niedioeflferramcntorum A liccrisindicatorum , tranfvrrf minmuro crypt^ firn:itcrdif- Ipoficorum, inferius in fcrrealamina propc Y codem modojquo in anrcccdeiitcdi<£lu,uCi{L- hicpercochlcasquadrifariam difpofitascotumlnfl-rumentum ritcad utiimadciptariqucac, iinaq; in faaconvolurionefirmitcrcontin€ri,nculrraplanumrequifiiiim diveilarur.. £fc' & lamin.i,dcquadixi,cumfuiscochleiscolurrtnqrotundcTlapidca^pcrBindicara'infi^itur, qux&cotam fuflinetmachinam, atquc profundcipfi ferra:inahaquoquebafi lapidca in- fillio. Habcc quoqus hoc ipfum Inflrumcncum . in muro cryprico circumcirca. tercci fuum etiam Horizonrcm Azimutbalcm T Y W torumOrichalcoinduduni &ii medioquafj muripofitum, quo Obfervacor flans infupcriori Gradu (Nam&hcclnfa"iv- mcnrumfi-Tos Graduscamcnticios, pcrquosafcendcndumacdefcendcndum. , proutcb- fcrvariorequiritjobcincc&ifua magnitucincexigic] Azimuiha, qua:perindiccsutrir>quc_^-| R &: S promuntur,numcrare queat, Diamcter hujus Horizonris Azimu:halis tantiis cfl, uc clrcum circd ulcra cotum Qiiadrantem , ipfumq; Quadratum & intrahunc tranfirc liccac: Ideoq; in fuaDiam.ctro 9 cubicos adaquac. Tf c; pcr fc totimi hoc Organum adcc;firm.iccr difpofKum ^: cochleismunicum, uc fcmcl re(flcordinatum vim rcboris humani>ucIoco di- movcatur,nonfacilcexcimefcac, Acquc ha:c dc InfliumcncihujusFabrica^difpcftiD- ne;quodetj.:m cocuminfupcrioremuri parictc^oqurdfrrL^fuccindccIabcratoab aeris injuriaprotegitun-. Hocetiam tedumfuashabecfcneflras, qua;apcriri poflunc, ^rotulii cedum porcantibus in quafvis Mundi plagas circumagi ; prout requirit obfcrvatio , fimulq; claudi , ddm Inilirumcntum ritc adapcatur, nevcntus perpcndicula cjns juxtaDanaturali ramitepervioIentiamdimoveat,£< infupcr, quandonulluseflInnrumentiufus,ucipfum ab injuna imbrium &: ventorum protegac. Atque ha:cquoad tcdum, in priorietjam QUa^ drantcefFedafunCiproucibidiximus, Usus ejuscumpriori idcmcfl incaplfcndis^ numcriandis tam alcicudinibustjuani B 4 Azimu* EXPLWATIO FABRJC^E eTVSt^S. Azimiuhis-,&ci"arcnushxcAl1:ronornijcinrerviunt,vcIiicianrainc!icacuni_,. Vcrumhic Qnadratiscumdio adjundoQii;Klraco,cum noii ialrcmtotus Mccariicus ric,&prioiem ma- irviimdineexccdac,adhucpaur6cxa(fliLisquamis,can-iAlcicudincsquamAzinuuhamani- feftac ; ica uc in fcxca cciam muiuci parccha-c pcr cum rimari dccur, ubi norirsimiim canca rc- iquiricur przecifio , prouc Hi_.'Solanmocuex Alcicudinc&; Dcciinacionecjuspcrrcrutando iOperxprcriumcA:. Addamvei6&hocColophonisloco,quodhirccduobusQv!adrantibus,anrcccacnrfl nimirum volubili, & hocChalibco cciam convolubili,adhibico una in tonriiiumQuadran- remaximoOrichalcico MuraH rivcTychonico(dequo poftcapracipuc confifi fucrimusm |Dcciinaciombu5Solisadamufsimpcrvefi:igandis,uchincejuslocus,cocumq;curriculum, Ifineerrorercfticuerccun-.. IdcmquoqucinDecIinacionibusSccllarum,quandOxMcridia- 'iiumcranribanc, rubciliccrrimandis,ubipra'cirioncfummaopu5crac,fad1iravimus. HarC cnimintriaingcnciaIn{trumencaricedifpofica,acqucufuiadapc?.ca,candcmecjamin cx:"iiisminuci particulis prarbebanc Alcitudinem, acqueunainidcmubiqi confeaciebanc^. Ojiibus ctjam Scxcantcs &alia Inftrumcnta tina adhibica tcllimoniuni fercbant-». SEMI- /* ^^^'^'^i^'^^'%i ^y^^^iS^"^., ^^sj^?»g^uzigegwE.V!'y^a3as SEMICIRCVLVS MAGNVS A2IMUTHALIS. £XPLl-\ EXPUCATIO TArBRlCAE ET VSVS. X coGiTA viMus & aliud quoddam Tnflrumcnt^im Alrirudinibusuna cum^ Azimurhisadamufsimcapicndisidoneum, cujusformamprjeccdcns indicacfi- gura->, Placuic aurcm i/.itcgrum Scmicirculum A BC loco Quadranris hic afiii- mcrc, & nihilominus juxta Diamcrri AC apud A , ccntrum Divifionum confti- tuere , c6 quod fic fmguli gradus inambitu Scmicirculi duplomajorcscvadaoc, quam fi cx cenrro cjufUcm difperririo fiar. Korum cnim eft cx Elcmcnris EuclideisangUlum a ccnrro circuli ad circumfcrcnriam duplo majorcm cflcco, qul acircumfcrcnriainhancipfanij. ducicur juxta propofirionem viccfimam libri tcrtii, & cas quxpra^rcrca huc conducunr. In mcdio hujus a centroD ufquein fuprcmum apiccm B canalis quidam cfl Quadracus oblon- gus, inrra qucm perpcndiculum , cujus plumbiim inforamine D cum aliquaparrc fJi Ori- chaIcicijmonilrar,quandoIni}rumcnrumpcrpcndicuIarircrercclumfir;itautpIanofcmi- circuIiverrica]i$,ornnin6corrcfpondcar.Contigriationes\Tio,quQhinciHdcabutraq:par- rc in formam Arcuu vifunrur, flabilimcnti faltcm loco adhibira: funr,ur vaflum hunc femi- circuluminfuoplano&circularidudufirmircrconrincanr. HabcrcnimisinDiametro A Cfcxcubitosr*. RcguIavcr6YAVipfiapp]icaracanramhabcrIongitudineab Ain V,quan- tacftfemicu-culidiamercr :&infupcrpromincntiam A Y paulocrafsiorcmureoccmmo- diLisquafiina:quilibiioReguIaatrolIi,depnrniq; pofsir:cujusctjamgratiaduomrinubriac foIidoMctalloapud Yaddicafunc^ Ab altcraVcro cjuspartcplumamcumcochlcah^ibcr juxra X, ubi in Quadrante parvo N O coercecur, ur in loco flaco, ubicunquc lubucric , pcr- rnancarRtgula,donccnnmerarafucric altitudo,inquacunq; limbihujusfemicirculipartc catunctranficrit« .Efl ctjamhocfemicircularcIn{lrumcr\tum undiquaq^ Orichalcicisla minis,proucopuscfi:,induOura,5chabctfupcriustresimagincsafi"abre infolidolignoarti- ficiosccxfcuiptas,atqueiradi(poficasin fuisiflhJcpcdcftalibuSjUcin figuraappnrct: idqucj ramornatusgratia, quami utaliquidctjaim (ua rcprixfcntationc hycroglyphice moncant» Eflenimfuprcm,aomnium,ipfiusUraniffin Aflronomaahycroglyphicumj. Virgocfbdc- cora 5c formofa.facie in Cailum fublata AfVra intucns , ac dcxccra manu Sphacram Ccckfliu 'rcvolutionumaccollcnsjfiniflrarapiens ea,quacamb^inferiorcsacqucfubcusflantcs, tan- quam pedifIcqu*c,porngunt. Colortunicxcjus cftCa-ruIcus^aureis^flelluIisintertcxtus.^Sc 'fimbriis argcntcis»Qiia: vcru iifmifVro latcrcfubfif\ir,GeomiCtria: Icon cfV: habens in dextcra !manutriangulum,qucmverfusAflrcnomiamatrolIit:inaIteravcr6Circinum:Quibusin- nucrc vulr, ic pcr commcnfuraticncm 6c fabricas maschanicas ; rum quoq; Trianguioriim_' 'crudiramfcicntiam Aftronomiainfcrviio* Hfccoculosinvultum Uranijcdirigif, earrq: vcncrabddafufpicit,CoIorVcfliscjUscflfubfufcUs,viridiinrcrrcxcus:qu6darcrreilribusdc- nommarioncm habcar. In capirefcrrumgerir laurcum,quooflcndic, fc fcinpcrdurric,&: verirarisintcmcratacapaccmcfrc^. Abaltcrapartc,dcxtcranimirumfubfiffensvirgo,A- ntmcthicamrcfcrt;qua:etjam Aflronomiamfufpiciens, honotar,cidenK};inicrvir. Kabc: h'a:cinalreramanucretam,alrcrarabcllam; fignificans,fenumcroscxprimcre;qiiibus A- fi:ronomia_,j ur cognirioni pateat,opus habct : caquc iii quantirares difcrccas rcfulvcrc, cux prior Gcomccria continuis expcdicbat. Habet & hax iuperius in capite fcrtum laureu ; c um non minus quam Gcometria pcrpctua & verax fio.Color vcflis aflaibus,pnpirUm vcl incm- branasrefcrcns;hincindevariiszyphrisconfisnatusr'» Atqucha:comnia,ut5c orn;uctur lnflrumentum,fimu]q;indicarctur,AflronomiamomniumliberaliumArtiumfuprem2m j& quafi Rcginam hafcc duas , Gcomctriam & Aritmcthicam tanquam miniflras, prx ca-tc ris,omnibus(licet&aliasnonncgligat)fibiadfciviflojnfrahunc ScmicirculumcftHori- zon Azimuthalis E F I GH quatUor cubitos in dimcticnre habens,cq; folido chalybe c6fl:ans & fupcrius in fuos Gradus, corundcmq; porriunculas aprc diflributus. Habetq; in mcdio duofortiafcrramenta,decuiratimfefeinccntroD intcrfccantia, circaquodctjam tctiim.» Inflrumcntum circumgyratur, appofitis ab altcra partc fuilciiraculis fcrreis,qua: illud pcr-. pcru6 Horizonti ad angulos re£lo$ contincant.Infra Horizonrcm fcrrcum funr quinq; co- Iumna:,quarummediaper Qj^ndicarainmcdirullioinfi-acenrrumconfiflir, rcliqujequa- tuorlitcrisPnotatarcircumfcrentiamaequalirer&quadnfariamdiilanrcsporranr, Habcnt infupcr omnes quinquc fupenus quafdam pcculiarcs cochlcas j pcrenncs nuncuparas,lite risq;Rfignatas^.Quodctjam inca:tcrisfubintelligcndum:qu«perparvamanUbriaSThiiic indecircumdudafurfumvcIdeorfumxtrudunrtirjdonccwrcuIusAzimuthalisiis innircns Horizonris etquilibrium cxacle imirerur ; & fcmicirculus fupcnlans planum alicujus vcirri- calir*. Poflunrcnimha;cochlecegravifsimumpondusminimoncgotioactollercvelctjam dcprimere,plurimamq; aliashabcntin M«Echanicis comodiratemj. Usus EXPLICA1 10 FABRJCAE er VSVS. U s u s Inftrumenti cx ipfafabricafatis parct: eflq; ixlcm cum iis,qua! alia-s pci-Azimutha &: Akitudit>cs£olliguntur:tiiriqu6dhicin$emicirculoiclc'mcffidtur&; numeratur,quod ifthicin Quadrantibusaut Regulis Azimuthalibus, dc quibuspoifleaagcm.us. Indicabo vcr66choc, quodcamantca QuadransiftechalibcusQuadraroincIurus (dequoinproxi-: meanccccdentisfigura: explicationcegimus ) ab in-itio , ut Chalybeo Horizonti, mferiore^ fuiparteinfiftercr,atqueineocircumduccrctur^. QuemadmoduminaIiafigura,hictamcn nonexpolkaoy^rimicuravimus^^VirumpofteacftconfultiuSseuintaliratiaac (proutan- tecedcns oftcndit figura) ab hoc Horizontali fulcro cxemptum circumrotare, eo, qiicd ni- mio fuo pondere ( cum totus fit , uci diiftum , chalybeus ) nimis comprcfse &: fortitcr Hori- zontiincumberct. Ideoq',difficillimecircumagipoirct , totamachinanonccmotaaut tre- mifccntcj. Potcn:nihiIominus5c ficejusinftituiadrniniftratio : tumq;nuIlo rotuii- do muro circumquaque opus efi: pro Circulo Azimurhali: uti nequcfcr- ramcntis fupcrius&inferius, velutiinpra:ccdentc. Dabimusfor- ^ealiquando&hujusdifpofitionislconaunacumfua cxphcationc: licctantcccdcnsratio longc cxpedicior & ccrciorcxiftau» 5£X- tt^mmmtamt^nmmdimmi INSTR VMENTVM RALLATICVM SIVE Repularum. PA- ■ EXPLI- EXPLICA1I0 FABRICAE STVSVS. NsTRUMENTUM IiocParalIacicum,quod alias Rcgulas vocancpcolcmai- caSjCtjam conficerc lubuicfiquidcm paucis rcquifitis, tribus nimirum regu- iisDiflanciaflrcllarumavcrticc; ideoq;&harumalticudincs fuccindc mcci- tut.. Accepi aucem ejufccmodi e lignea falccm maceria totalitcr conftans , quodolimfucracincomparabilisillius Copernici; adcoque ipfiusmanibus (ucidiccbacur) claboracumquod mihidonomifTumeftaDominoJohannc Hannovio, Canonico Warmienfi, ubi ancca vixerac Copernicus : Cum anno i^g^.quendam c ftudiofis meis in cxcrcitiis Aflronomicis mihi infcrvicntibus cum Scxtance ad mllar ejus , quicercioIocofupcriusclucidacusen:,c6ablegailem,ucEIcvacioncmPoli,qui WarmiiEcfl:, exaillifsimc, hoc intcrmcdiantc dimecirctur^, Sufpicabar enim tria proxime minuta in Copcrnici circa hanc obfcrvationc defidcrari ; dc quo mocus Solis ,& Ecclipticse obliqui tas maximaaliccrfchabcntia,quamipfiusfnppeditantnumeri,mecommoncfeccrunc. Quod & ipfa cxpcricncia,ita fc habcrc comprobavic.Invenca Cil cnmi raco Organo cxplurimis cam adfixasquamSolfimhabicis animadvcrfionibus, Poliifthicfublimitaspartium 54, M.22;J. Utilatius a nobis inPrcgymnafmatum AftronomicorumTomoprimo pagina_. 34,&fc- quenti dcmonftratum elt: quo in lococaufas iapfus Copernici inmotu Solis nonriceab ipfo rcdintcgrato oflendo, Praifuppofuic vero Copcrnicus cjus loci Laticudinem ex fua ob- fcrvacioncparc; 54*M. ipj, Dcficiuncigicurapud ipfumab cxa:imam, quit concingic in plcnilunij s, non candem cifc , qua? m Quadraturis ; notabili intcrccdentci diiterentia,utpocc,qu»eccrLiamGraduiparccm.atcingac:proucifl:hiclatiusperiuascircum-. flantins Scoccafioncs vidcrc cfV^Angulus autcm diftanciara vcrticcFDE habcri poccflcxCa- none fa-cundo auc ccjam Sinuum intcrmcdian tibus parcibus F E.Dancur cnim in Triangu- lo duo ajqualia laccra F D & E D. Tcrcium vcro F E in rcgula longiorc pcra^fla obfcrracionc numcratur. Quara angulus F D E latcre non poccfl, qui rcmocioncm Sidcris a Zcnith meti- cui\ Ejus vcro com plcmcntum ad Quadrantem cfl altitudo quxfita, Habcnth^ Rcgu]sc& hoc com.moditatis , utfacili ncgotio rcfolvi 5c complicari qucanc , atq; in quxvis loca tranf- porcari.Vcrum,ucdicam id quod rcs efl,eam pr.rcirioncm & ccrcidincm facis conftan» tcr non pra;bcnc,qualicunq; candcm diligcncia claboracx, quam Quadranccs an- tcdidi.DiiliciUimccnimRcgulaclincacrcdaeamufsimdmrccinenc.Ecfilon. ^iorcsfuerinc, fuopondercfcindcrcclinajio» Sinbrcviorcs,id quodpolliccnturfua parvicacc prjcflaro nequcunt.'. 1>AK^L' mmmmmmmfiimrr. PARALLATICVM ALIVD, SIVE KEGULM TAM ALTITUDINES QjaAM A zimutha expedientes. c » EXPL7 ■m II -i I w» '> EXPLICATIO FA^BRICAE ET FSVS. Go vcroannisaliquocanccaaliasRcguIasln Turri qiiadam cxtruxcram, eam co- f ram fua circumgyrationc,quancio opus crar,adimplcnrcs. Idq; pcculiari quadam IJ^^racionc, parcim Hipparchianum vccuftifsimum ( ucfcrcur) modum imiranto; parcim vcro novis additionibus a mc ipfo cxcogicacis (labiliori & commodiori ufuidcftinacas: quarumftruduramfcquens rcprarfencac figura: in qu^ AD in- cclligacurprima&fundamcncalisrcgula adHori2oncisplanumdi(pofica_,, &:proucopu5 fucric,rcvoluca: qua^fua longicudinc e^ cubicosadscquac: Concinctqiinfupcriorifuafu- pcrficiccanonis finuumnumcros arcificialitcrpcrpundatranfvcrfaliamcomorcdivifus, fex Zyphrarum, bis numcratos^.Huic ada^quantur binjc alia: rcguljc fimul fumprz : cum vi- dclicct cidcm applicantur : nempe A B & B C« quarum quzclibcc 4 J cubicos in longicudino continct» Anneftiturvcroprior ABprincipiolongiorisjuxtaA, itautin co accolli dcori- miq-,pofsic,fimulq-,fccumcrahcrcpoflcriorcmBCeidcmjuxcaBconvoIubilircraffixo.* In hifcc auccm duabus minoribus rcgulis nuIla:funtdivifioncs , fcdpriorfaltcm A B habcc dioptras & pinnacidia,pcr quae collimatio fit,rimulis in infcriori pinnacidio juxtt oculum adT£; ultcriori ad F,undiquaqq;parallcli§ : uc tam in Altitudinibus quam Azimuthis quaqua vcrfumcircahjecfiatcollincatio, Omncsautcm ha;trcsRcguIqubiquc Orichalcicjcfunc, fubtilifsimclcvigataj&cxpolicx^quadrilaccramjuftamagnicudincneincurvacioniobno- xia^finc, obtinenccsformani->.Ucvcr6commodius,quoadduasfupcriorcs,accollircmicti- qucpofsinc,addicumcftiiliscxtans qua-damfuftcncaculumpcrLNOP indicarum, quod crjam infcnus luum habec fulcimcnrum,rcpraf fcnrarum pcr P V Z Juxra V vcro cftCochlca, quxipfum fulcimencuminfubftrudococius Inftrumcncibafimcnco(dcqu6poflca)a*i W circularem lammam undiquaq; dirigic, nc fuo fe pondcrc aggravcc.Excansauccm verfus Zcnithftru£turaidhabcccommodi,ucrcgulasfupremas (proucdixi) accollac,cafdcmquc pro Iibito rcmiccac unaq; in fiio plano, nc hinc indc diftrahanrur, coerccau» Accolluncur auccm & rcmiccuntur inccrmcdiancc funiculo K LN M, qui f uperius juxca L N roculam ha- bet in qua apce crahicur : idemq; primac rcgula; anncdicur juxca K , ubifuppofica mccallica.^ figuracio, qu£c in clavo rocundo convolvicur, adco inccrius paccns cft , uc pinnacidium ad f cxcculojuxtadioptram E undiquaq;nulloobftaculo difcerniqucat. Habcc&hoccom- modi uc pcr pcrpcndi cul um, quod in Q_dcfinic, Inftrumcncum ficum cxaminec : an vidcli- cecADHorizoncemcxa£lercfpicic: LNPOeidcmfic Orthogonalissr'. Quamvisidipfum quoquc cx pcrpediculo B R fcrutari liceat. Dcbet enim id ubiq; intermcdium cfTc A & C» Porr6qu6commodicsattollanturRcgul^,atqueinftatuloco(proutlubucric)quiefcanc, tum quoquc, nc hinc indc vacillcnc, fcd idcm planum cuminfcriori &Iongiori fubftancia ubiq; recincanc : quomodocunq; furfum vel dcorfum agantUL. Additi funt illis ucrinquc duoQyadrantcsIHG,intraquosprior Rcgula conrinctur&movctur, appofitaplumula tcnaci juxta H,funtq; hi Quadrantcs Orichalcicis laminis udiquaq; indufti.Habetq; a ccntro A ufquc in circumfcrcntiam I fcrc trcs cubitosr'. Dcmum ubi Divifioncspcrada obfcrvatio- ncjuxta Ccxcmph loco numcrandae funt, acutifsime pcrchalybcum indiccm ifthic indi- cantur, ut ucrinq; juxta C plumula; func chalibcap,qusc ccjam in concincndo rcgulam B C nc fua gravicacc rccidac, juvanu* Pra^cercafulcrumfivc bafimcncum (dcquo antcadixi) inquococumlnftrum.cncum ab una parcc, pracfcrcim poftcriore quiefcic, & circumgyratur, Pcr X W intclligcndum crit, in quo fupcrius juxra T cochlca cft pcrennis , inftar carum dc quibus antca in Inftrumento fcmicirculari dixi , qua^ pcr manubrium ad T fublata & dcprc ffa , cocum quoquc hoc Orga- num rice dirigic; ica uc infcrior & 15gifsimaRcgula Horizoncis plan6 cxadecorrcfpondcac, plancq;conveniat^,TandcmeciamcxcimaRcgulaeparsDmurocircuIariincumbic,quipcr liccras Y cxprimicur:Habccq; fub fc in codcm Muro firmo circulum Azimuchalcm Orichal- cicum, convcnicnccr fubdivifum, 6c fnpcrficici Horizoncis analogum, corrcfpondcn- ccmq; Alcicudini , quac cft prioris bafimcnci : Eftq; in Diamccro duodccimo cubuorum_.» Ufuscociuslnftrumcncicft is,ucillius bcncficio cam Alcicudincs (pcripfasnimirum Rcgulas, ubi vidcliccc infimam accingic) pandac; quam ipfa Azimucha,ubi cjufdcm cxcrcmi- cas propc indiccm apud D, Azimuchalcm Hcrizoncem flringic & nocac»AIcicudincs vcro fic habencur: Cumambolaccra duarumregularum AB&BC iequaliafinc,ccrciumq;AC ^c- cundumObfcrvacionem&numeracioncmconftec: ignorari ncquic, Angulus BAC, Alci- lcudincmquaeficamcxhibcnsr'. IdcmaIiaracioncpcrficicur,finumcrccur,ubipcrpcndicu lum BRinfcriorcm rcgulam infuis divifionihusaccingic, fado inicioab A^Tunc enim da- cur EXTLlCoATlO F^A^BRIC^iAE ET FSVS. daturTrianguIum rcftangulum; cujusunumjlatus cognitum cx flruftura , altcrum mu meratum fccundum Obfcrvationcmj. Quare anguiusad A , quiqua*rebatur,ignorari ncquic, Quorfumvcro Alticudines&: Azimuchapercineant, cpragrnacica Aftronomica-/ difccndum,proucanccainrinuavimu$^. Hoclnftrumcncumobquancitatcm&longiciidincm priorcsRcguIascxccdcns, prar- ciriusomniaexhibcc', magisq; flabilc &|uU]i aptum eft: prserertim quoad Altitudincs ca- iendasr', In Azimuthiscnimundrimandis ahquarubeftdifhcultasobipfam Inftrumenti magnitudinem 6c moIem.Quac tamen adhibita aliquali diligcncia pra^cavcri potcftata uc in- fenorRcguIa ance Obrervacionem IcolIocecur,&figuratur immobilisinccrcoaliquoAzi- mucho, verfusquodfidusobrervandum vcrgit: &tancapudperpcndiculaprovideatUL,! ancequam Altitudo accipitur; ut omniarite difpofitafmt, tam fccundum cEquili- brium Horizoncis, quam planum vercicalcj»* Tunc enmi & Alticudo &; Azimuthumcircaerrorcmfenfibilemdepromihoclnflru- mcncopoterinc, nonminus quam Quadranci- bus.maximis fupenus cx- planacir^^ t i ARMIL- ;^;N§t^Jji?^<^^i^ ARMILL2E ZODIACALES. EXPI. /- ^ « r III iJlii EXFLlCtATiO FiA^BRIME ET VSVS. R G AN A anceccdenna€6potifsimumfpc^ant,ucAIcicudincs, & Azimu- charivcrcorrim,riveconjun6tim, iis Coclitusobfcrvencur. Quia vcrohoru in ufum Aftronomicum dcdudio prjccipua cx parcc caJculo indigcc Tri- anguIorum,non omnibus faciJc obvio, & pcr fc quibufdam Jaborcm ciFu- 5iencibusca:dioro,cxcogicata:runcaIiasmachin2e,quibusjflcJJarum Jongi- cudincs & Jaticudines, qua: duo principaJiccr inquiruncur, minimo ncgo- cio & abfque moJefla caJcuJacionc habcri qucunc;inccr qu2c,duo prarcipuc vcceribus in ufu fuiflTc comperio; quorum unum ArmiJJarc Inflrumcncum appcJJabanc, quod Hipparcho &:PcoJcma^o in ufu cracjdeoq; ab iis dcnominacionemforcicum.AJcerum Torquecumdidumcfl,abArabibusaucChaJd2eis (ucicxiflimo) cxcogicacumOrganum,| iisq; ufurpacumj. Idq; in planis fupcrficiebus circularibus idem prxflac,qu6d prius in Ar- miiIis,Hocauccmpoflerius, nec dumconficrivolui,quia>., fimachinarcquifitamhabcac magnicudincm,fuo fe pondere aggravet,atque ufui inhabiJis fic. Cujus nihiJominus fabrica^ fiqLiisdefidcrac,Opus Aftronomicum Cacfarcum AppianicircafincmconfuIac,fivcScho- nen]ibcllumdeeodcm,ObfcrvacionibusCJemcnciir»viriRegiomontani,acqucipfiusdifci- puliWalccri civisNorinbcrgcnfis prxfixum, Ibivocicomposrcddccur* ArmilJarcvero 'jamdudumconficicuravi Inftrumcncum, inquononnuJJaabHipparcho& Pcolemqo u- furpacaccrtioriscommodicacisgratia immutavi: CujusIdeamJiicconfpicis, Conflachoc Inftrumentum quatuor faltcm Armillis circularibus (cumprxdcccfrorcsquinqucvcl ^tiL adhibuerint ) quarum prima£ B G N H Meridianum repr^fentao* Dcbctq; difponi ut Coe- Jefl:ificanaIogaJnquajuxcaCDpolifuncaiquatoris,quiatcolIuncurdcprimuncurq;,donec Iacicudmicjusloci,inquoficObfcrvatiocxa(n:ccorrefpondeanc.QuodperperpcndicuIum BS exploracurappenfumfuperius juxtaZenith, ubidivifioMcridiani complcmentum ha- bet A}ticudinisPoli,&; tantundemetiaminfcriusaPoioalteroremovccuii,.Concinecaucem hic Meridianus omnes alias incra fc Armillas : quarum prima eft C F I H, Zodiacalem aJcera P O QJT cranfverfim porcans, cujus Poli funt apud I K, Cflncum. diflanccs a prius didis lequi- noo,Gradusdivifi,&quiIibct horum in 60. mi- nutamorc nobis ufltato&firpiiispcrpun^flarranfvcrfaliaindicato, Alccravcro Armilla-» tranfvcrfalis,qitarndixiiEquatorismuniafufHncrc, pcr HLKI oflcnditur: quarctjrmin duobus oppofitis locis Mcridiano fupra d\S:o apud C,&: illi Diamctrali firmitcr annciftirur, arq; cidem adamu(sim ad angulos rc£los infitlit, inq; co imrhotus quicfcir. Eflq; ctia ab cx- feriorefuiparrcinomnesCirculiGraduscorundemc];minurafubriIircrdiflributa_.,Acha- berquaruorpinnacidiaparircrfa(f}a, urin priorc:quorumduoIKinunafcmicirculiparr« hlccxprimuncun^.RcliquaduoinaltcrohcmicycloparircrinrcIligcndavcniunt. Suntq;o- mniapinnacidiaexOrichalcoaifabrcclaborara.-ipfcq;Meridianustorusefl:efolidochalibc, urfuftincnrisrcliquisinrerioribusfitfuflRcicns. Armillaj%'crobina: decuflatimfclcintra hunctranfcunte5jabpo(lcriori(dequadidum)fbIummod6fuipartclaminafortiOrichak cicaimbura?funT,inquacriam'divifionescxin:unr;Ncqnccnimundiquaqu II II 1 1 ARMILLiE ALIyE AEQVA- TORl^. I nmnitrt JiiiJn Exni EXPLICATiO FABRICAE €T FSFS. L I A s quoquc cjufdcm quanticatis Armillas conficri curavi i^qiiatorias,quarum Ideam hicvides.Exterior ArmillaiMeridianum (uti&ancca ) rcprarfcntat. Iflq; cotaChaIybca,adamursim undiquaq;Jcvigata, &DivirionibustotiCircuIocom petcnribus,ita ut fingula cdam contincat Minuta, dift:ributa_..In qua ca^tera quo que, quoad pcrpcndiculum, Polos & Axem intclligenda veniunc ; prout in prioribus. Qux vcrointrahanccontincncur, trcs funt Armilia:, ita ut totumOrganum^. conllec, unoam- pliusquamantcccdcns: pra-tcr Axem terctcm atque Cylindrum illi infixum : quarctjdm u- nius Armilla; vices commodc fuppIent.Habct autcm hoc Inflrumentum propccrea tresAr- millasinteriorcs, cxccptoMcridiano, eo quod i5^.quator fic circumvoIubiIis,nonaucem' quicfccns,utinpriori.Ideoq;ArmiIIaIFG Hindiget,eamfuftcntantc,&Ortho5onaliter' cohibcatcquccctiamcpuro conftac Chalybc, quofortioradidinunuscxiftac^nullis tame diftinaionibusinfignita... Ipfcvcr6^quator,dequodixi,perPSR indicatus,fuashabec divifioncs ufqucin fin^ulaminuca,&cas quidcm tam ab unaquamaltcrafupcrficie; prouc YelyEquacoriisdillanciis, vclcciam ccmporariis momcncis difccrnendisulijs poftular : & piitiiacidia illi adapcaca func juxca R & P, cum quoquc plurahi c non cffonnaca ,qux obfer- nalicercranfit^convoIubiliSjUcinlocofuicontacluspunaaetjam/^-quaconaindicctcon. vcnicncibus laminulis iuxta S &.xM pofitis. Habcr infuper fua pinnacidia juxca CL& O & duo aIiahicnondepiaa:fedpariccrabaitcrapartciateIJigenda_,, Divifionesquoq;inrunc,fn- gulisQuadrantibus minucacimcompetentes. Omncsautcmilla; Armill^MiuraMcridia- numcorapra:henfa;funtundiqaaqueOrichalcicisl?:rninislliperij)duaa:;idq;tacafubci]ita- iT&levigutione,iicdicerescocasrf]ccxfoIidofufasOricha'co, Axisquoquc teres Orichal- ;c;caiieft,uci&iprapinnacidia_,.PcrpendicuIumRTefiloconft:attcnuiOnchaIcico,prouc aiiasnobismoriseft:. Ccccrafiqnjehicomifla, cxipib intuitua/lequcris,prcutctjamin_. prioribus, IncunnbuntharArmiilx fuftcntaculofivcpedcftali e folido Chalybc ccnftanti: quod pcr X T V Y Z,rcliquasq; inter pofitas Jiteras dcfignatur : Cujus fuperiorpars fvmicir- cularis cy.G\YY ipfuni Meridianum rcliquas Armillas comprehcndente.abinferioriparte^ coiinnucambic 5c fuflinct;additis quatuortcnaculis,uti&inprioi. Rcliqiiaformahujiis' peJcftalisfatiscxiipfafiguraliquctiubiqua-dampr^rtcrutilitacem&corrcboratiorempul chiitudinis caufa laddita funt ; qua: tamen & ipfa hilcimcnta prxbcrt t;omniaq; €x fblidcuTci &anteadiaum) conftiatchalybc^, Infimusq;hisfubftracusCirculusZ crafius&fcrreus,a quacuor fuis y^qraidiftantibus Jocis cochlcashabeo : Quibusinquadracolapide fubftcr- nu:icurqua'damp)arvaferramenta,uciniiscochlca;barcircumduaa*totumInft:run^€nHim c6diriganc,quo Armillct Coelcftibus anaJoga* reqununcu: Idc];inrcimcdiantepcrpcrd<- culoBT,quod&planummcridianiMiechanicicumCoclcftiunif,5:cjus infupcrdifpofi-j tionem rationcElevationis Poli ordinat : adcoq; omncs intenores ArmilJas Ccelcftbus Circuli3.qnosa:muIantur,anaIogasreddit, Eftci;totamachinainreipfafatisrobufta,necaU ceracionitaciIeobnoxia,cumundiquaq;metallicafic^. 11 s u s ejus cft fimilis cum priori , nifi quod hic i^quator , pro lubito rcvolvarur intra Mcridianum.Dcclinationcsaccipianturparitcr>ucipriusinArmil]aDcclinationum,apud fiiumCylindrumiuxtaAccnciMlcmpcrpinnacidiaconveniencia_.. .^.quaroriarDiftanria, fiveafccnfionesrcaa:inArmill3franfvcrfaa:quatoriaprouc&antca,nifiquodhiccjusAr. milla: ChalybciC, qua: has ipfas portac, aliquis ctjam uflis m hac pragmaccia efle qucac. Acce- dic&hoccommodi,qu6dquandoficllaa:liquainfiiadcbiraafccnfionerct©?;uo7roAiTHV, ita uc, ii n .ccUitas & uflis po(lulet,non uni alicui Rcgioni ita adftrj(flus fit,quin alio ctjam migra- re, i-c ibafecumfcrrelnflrumentaliberc&Iubenccrvclit&pofsio. Curocnimpaucifsimi ii!it)quihifcearduisdifciplinis&cxercitiisoccupcntur>& rai:ifsimcinterPolicicos,quiRei- publics adminiflrationipra-cHevolunc, invenianturaliqui, quihisimpenfcdeledcncur, eiqifovcrc&fuflcntarcconfultum ducanc; fcdlongepIurcs,quica obignoranciamavcr- faiicurarq-, inutilia a:fVimanc;nonoporccc Divinae Aftronomiacalumnumcalibusimpcri- jd« iudicu«.nhnoxiumcf!e, fcd ca cx altc ncgligerc ,& nihil facias cxiftimarc,qu:im hifccin- |vic!:ilare{ludiisjnihilq-, alioruramovcriimporcunicacibur', Cumq^nimisfuncmolcfli.fivc poncjci livc aliiilef uaq', alio transfcrrc : adco uc nc nacalc quidcmjfolum , quod dulccdinc (cundos rJlicic, iramcmorcmnec finiceflcfui;hifcc CocIcflibus&fubIimibuscuris,qua: immorcaliracis vcftigia prsefcferunc anccponcrcdoceat: fedconflanci&pcrfcveranciani-. nio fcmpcrinomncmrcrumcvcntumiecumcogicarc,quod %)ndiq^ terra trjjrajCcelHWpatet undic^fH^ra^ Etpatria eBfortt qtulibet ora *viro. JRMIL- ^^m® ARMILL.£ AEaVATORI^ MA-' XIMiE, SESCLVIALTERO CONSTAN- tes circulo. HWaMMM © EXPLI- EXPLlCATlO FA^BRICAE ET VSVS. I^^^Tsi binx machinarArmillarum aquaroriarum jam antea dcpiiflar & expoficar, ^J te^>||(qiiarccjam magno nobis confticcrunt) illi,dcquociixi uruifatisexacleinfervianc, ^ [3S3 iJinvcni nihilominuspoftca & conflrui curavi, alias quafdam paucioribus rc ^quiritisindigcntcsjucpoceunicarolummodoArmillaincrc^raconvolubilij&al- teraiemicirculariquiclccntc-). Qu^ibusduabus omnia,qua;deprioribusdixi,nonraltem commodc, cxpcdiuntur; (ed & longcpromptius, nulloq; obftaculo; quod antcccdentes in- gcrunt, fi prope ipfam Arnullam Aquatoriam fieri debet collimatio, Tunc cnim anteriof cjusparsintuitui obftat: qucmadmodum ecjamin DecIinationumArmillapropcipfum-j. ^quatoremdifficilisfitcollimatiojutdcaliisquibufdam impcdimcntisnondicam. Ha- LenchsarLcra^idinfupcrpra-rogatiya^/quodlf-ino^pn-ifljore.sr.onficiqiieanC! Ideoq;Gr3du« cumfuis divifionibus magisadhucdifcrcteexhibcri , &nihiIominusfuaftabilitatc&con- vo!utioneufuiaccommod?ieflc; idquefaciliusquamantcccdentesr', Formavcroharum ingcntium&: apprimecompendiofarum Armillarumhhisq; intcrmixra circa L,5c deinccps repritfencata interponuntucccnti- gnationis, acfuftentaculigratiaadditafunt, tumquoqueornatus. Inniciturverohocln- , itrumcncum fulcro teren & craflTo, quod per T R S Q^ionftracur : habens in medio , ubi a-- jquiIibriumefl,juxcaEfQramenquadratum,inquo fiiofulcro inquadrara etjam claviculu iimponicun.. Fulcrum veroficfehabcc; utjuxca S& T, tumquoqueQ&R finc rotundi^ |]aminjcferrca^,quainfubfl:ratoccrrtiCyIindro, fpitamum adminimum in Diamctro ha- jbcntcconvolvitur, plumulis equatuor partibus tenaciter ipfum , ut quovis in fitu facile fubfiftatfuflincnnbus. Volviturautemhacrarioneipfumlnftrumcntumfolummodofur- fum atque deorfum_s,Si vero adlatus inclinandum vel reclinandum fir; id fiet: circum.dudo femicircuIoONM,&firmatacochIeaiuxtaN. Sicenim unatotumfevertirlnftrumenru, Poceft etjam pcr canalem P V , cui in rotundo axe i nftat , hinc inde in omnes Cali partcs c6- voIvi.CanahsautemilIiaIiipcdeftaIiperV&Iiter.as Xfignincato infiftit, inquoetiamun- diquaq;cumcoco Inftrumenco,prouc6pus fucrit, circumvcrcicur, ucid in planum qua- rumvis ftellarum dirigi pofsic: prout Obfervarion is rario requirir. Poteftcrjam ejufdem ca- nalis inrerior Axis unacum ipfo,acieon; innirrnrirlnn^riimcp.co^.Iciiis infi]bjc'fto p^defb-^li attoIli,acq;ficfigiimmoteproutufusexigit.DefcenditenimintraquadriIaterampedcfta]is formamquadrilaterumquoquefolidumlignum,quodfurfumferriatq;remifti,&:ubicun- qucluberfirmaripoten:;ficq;unaartolIiveI depri milnftrumenrum, veluri ftcllje,quarum intcrcapedorimanda,aItioresveIdecIiviorcsinCoeIofucrinf. InipfoautemIn(irumento, quoadlimbosubidivifiones functumqnoqueinTranfvcrfali&: Cylindris,omniafuntOri- chalcica. Contignationes&fuIcraexferramentisafFabrcelaboraris. Reliqualigneafoler- ter compofita& metallicis laminulis , ubi opus eft, munita, quo totum Inftrumcntum fir- mum fic& Obfervationibus idoncunij* Ususejuseft(uridixi)inminoribusdiftantiis commodedimetiendis; fiquidemin fexcance ( dc quo poftca) qui duos ecjam Obfervacores requiric id apce praftari nequeacob capicum conjun6tionem, qua^ conveniens fpatium exigic : licec & alio quodam medio huic incomniodofubvenerimus:Dequodeinceps. Vcvero intercapedinesfiderum,qua;duo- decimamcirculiparcemnonexcedunchoc Organodenoccncur, firmerunusObfervacor pinnacidium apud K vel Lprouc maximc conveiiiensfueric : & alter id quod firmacum non efl,crahac in ulceriore Iimbc>,donec fic ambo, titina s quas rimancucftellas circa B & A Cylin- drosucrinq; confpexerinc; quodlibec adfuumCylindrum in eademparce attendence: & numerada eft in inferiore linibo diftantia quas quicrebatucinGradibus atquc minutis trand verfalibusjuxtaconvenienspinnacidiumj, Si veroamboutrunquediftraxerinr, nnnm.o- do poterit adhuc majorintcrcapcdo,qujE camen limitem praefcriptum non excedat, con - /taro, Confe£iarium igiturevadit, quodubi amboObfervatores utrunquepirtnacidium jux:caipfuminitiumDivifionum,quodeftapud K &I, difpofuerint,&ficutrinquepcrCy- D 4 lindros EXPLICATIO FABRICAE ST FSFS. lindros antcriorcs A B coUimationcm inftitucrint, ita iic quilibct fuum rcfpiciar, ab ^adem partelonga:Rcgula:dirporitum,quodtunccandcmftellamcollincnc; fiquidcm para^leli- ccrvirumdirigant. Atquchincpotcflcxplorarilnflrumcnticcrtitudo, an ritc fe habeat necne. Etfivcro hujus Inflrumcntifulcrumrivc pcdcftalefatis commodum ,iS: ufibusre quifitisaptumfititamen altcraratio, qua^inglobofoficcorporc (dcquapofteainSexcan- cis expofitione dicemus ) adhuchabilior eft ,-& cicius planum quarumvis flc!larum Inftru- mencum dirigi concedit-^» Scdvarictas tamen inhis,non folumdeledac,fed5:fuamha- bcc utilitatcm_9. Tj/-.r-TnnTnm.-nro*"vnlrirflvinonr«imnm ftcllarum inCafsioDrraadin\M;(-(.rn diOnnrinsV' quzeexponuncurinProgymnafmatumnoflrorumAltronomia?mfi:auranda:capicequarto! pag.Hl^acquefcqucnti; easq-,cum priiis adinvencis, dumadhucdurarecnova ilclla, cujus' granailla^ pocifsimum deprompca; funt, contuli , acque ritefc haberc depra;hendi. Si quis; hiflrumentumquodcunq; habuerit, quofediflanciasSiderUmrimaripoflccxiflimet, fa- ciacpenculuminiifdem Cafsiopara^Stcllis, an eandem, quamcicaco locoannocavi- mus, invencric illarum inccrcapcdincm, in ipfb Minuco,adebq-,cjus fe- mifso. Alias fciac, Inftrumencum illud, quo ucitur, & obicrvandi racionem nequaquam rc- i^econftaro. SEX- SEXTANS ASTRONOMICVS TRIGONICVS PRO DISTANTIIS iimandis. ■^IMMWllil I I I TiAlHiw EXPLl- i EXPIICATJO. FJ2RJCJE ET FSFS. Enio niincadfcxtantis Aflronomici cxplicationcm, quatcnus is intcrcapcdi- aibus Sidcrum coelicus fcrutandisapprimc idoncus cft^Cum cnimRadium Aftro- lomicum huic officio, ca qua par cftjpra^cifionc & ccrtitudine ncquaquani f ufH- jcrc,multaplurium*annorumexpcricntia compcrtum habercm, neccfsitarcur pcncecxcogitavirexantcsquordam,variaforma,quiidcitra omnemhallucinarionemcx- adc pra-ftarent, intcr quos hi,cam, quamccrnis, compofitioncm refcrcntcs,mihi confimo- . Poceftq; una cocum hoc In- (Irumcncum cam quoad ipfum fcxcanccm,quam cjus fulcrum convcnicn- dbus cochlcis disjungi , rurfumq; componi; uc cifta inclufum in alias, ubi opus fucric,rcgibncs cransfcrri queac : qucmadmodum ccjam a nobis anrc annoscirciccr 24, cumGermaniam cranfircmus, in juventuccfadumcft. Ejus verofabricacxipfafigurauccunqipaccc: Plcniorcm Explicacioncmfummacim hicrc- pecicam addemus cxlibro noftrofecundo Progymnafmacum ; ubijuxca calcem idem In- ftrumencum,&confignacurh&:cxpoficurn,ScxcansipfepcrABCD rcpracfcnracur&juxca A ipfius ccncrum eft,cujus Arcus B D in fexaginta Gradus corundemq; fmgula minura mo- re per cranlvcrfales Imcas nobis familiari divifus. Regula: Inftru mcnci A B & B C in A circa clavum rocundum coapcantur,uc ampliari vcl coarftari inftar circini quear: idq;perco. chlcam liceris G H mdicacam^quas quamvis dircclft fic,camen in parcc qua Rcgulis ad harrcc, marricibusundiquaq;mobiUbusficaffigicur, uc Arcuali Inftrumenci morui nihilofccius tinferviac.Habccquoq;duomanubriaIicerisIKfignaca, quibusincer collimandumlnftru- imciuum apprchendirur.B & C func duo pinnacidia, circa qua: oculus adO prope Cencrum Idircdus, duasftcilasfimulobfcrvac;bcncficiocpchlcitGH,anguluBACampIiando, velco- Lr6tado ubi Arcus BCDiftancia quacficam oftcndic,nifi quod Parallaxis Inftrumeci provcnies [hinc fubcrahenda fic. Quavis aliud quoddam mediu poftca invencrirn,uc parallcliccr fiar col- lineario , non minus quam in carceris diopcris & pmnacidiis : ficq; Parallaxcos fubcradionc jnon cric opus,Verum quia ha:c diopcrarum racio li,ic non eft reprccfencaca,alibi camcxplica redecrevimus-.Ubi hicipfefcxcansiisinfignitur. EcinfupcrpedcftaIehabcr,inquoadhuc fcxcans commodius in quodvis planum dirigiruiL.. Eft auccm hujus fcxcancis urraq; Regula I A B & A C cubicorum circiter rrium,quibus Arcus ipfius B D fubccnfa coarquacur.Eftq; co- cus hic fcxcans e folido chalibe afFabre claboratus,nifi quod pinnacidia func Orichalcica ; & fulcro cuidam incumbic, quo magis ufui apcus & inccr obiervandum cradlabilior fit-». Ful • crum aucem & pcdeftalc in hunc modum fe habcc:Primum,juxta V X Y Z bafin decuflatam, Terriefirmiccrinfiftic:cuiproximumquaficruscavumeftadT, uclongaqu^damcochlea ad Qm illud dcfcendac,qua: pcraliam perenncm di£lam,intraP cqnclulam, prouc opus ac tollicur vel dcprimitur; unaq; ipfc fexcans.Ucraq; vcro cochlca e folido ferri mecalIo,qucm- admodiim h. cocafuperior fulcri pars, conftac. Tcrcs veroferrum A O inrcrius cavum, cir- caaliumoblongum Axemipficochleaj Q^,intermedianreibidemapparenre capicelloinfi- gmcum,equo apexquidamegreditur, cui aliud longumfcrrumlircris LM oftenfum ad- h r<»»-i 1 ic rr«r n liriirr» 1 rf iriri O Ifr^ concinnacum , uc quando ipfius cochlea ad N vercicur, tum apex ille per inceriorem rocu- lamoblongumferrumLMUnacumcocofibi inhaerencefextante adbinarumftellarumfi- cum hincindclaccraliccrinclinec. PerArcumquoque SR ipficerccifcrroOH^dcquodi dum circa S pcculiari junftura infercum cencrum ad A poficum una cum ipfo fexcancc clc- vacuracrcmitcicur, proucAlcitudovel declivicasftella; poftulac,firmacuiq;uclibcc,ineo- dem Arcupcrcochleamabalrcraparrejuxcap.adjunc^am-j^Scdhaxomnia oculari incuicu |&cradacioncmcliuspercipiunruL,Hocquidcmlnftrumcnco,quodanccpIurimosannos confici curavi, inccrcapedines Siderum fcrucariis fum : Eracq; cjus maximus ufus in Obfer- vacionibus Comcca? anni 77* Quare erjam in libro, quem luculcncer dc eodem confcripfi- mus, circa fincm ( uri dixi ) confignacus hic fexcans uberius defcribicur, Si quis volec, plura ibidcm a pagma 4^9. ufquc ad pag.46i,dc eodem legao. U s u s ejus eft pro capiendis Aftrorum diftanciis incra fexcam Circuli parccm idquc ab unoroIummod6obfervacorc,quiappUcacooculoaclCencrum A,&cocofexcanrcperfulcri cochleas in eorudcm planumdifpofico circumagic cochleam G H,in quamvis parcem: ficq ampIiacauccoardacangulumB A C donec incrapinnacidiaBC utraqueftella exaftilsimc colIineGtun-., Monftrabiccnimtunc divifio arcus B D inccrcapedinemquxqu3Erebarur_.. Habuicverocircumferenciaejusabiniciononfalcemdivifionemvulgaremjfed&Nonnia- nam-j, Verum ciim ego ipfa cxperienciacdoccrer, aliam pcr pundla cranr-frrali^^mulco commodiorem& acurarioremefie.,', pofthabitis hifce, eapoftmodumufus fum,& cir- cumfcrcnciamfexcantisOrichalcicamfeci,ucrubigini,proucChalybs,nonforecobnoxius: E acdiftri EXPLlC.» it«^jjwl.*.«..i . 1- , v.j..-»»-..wwA-i i »-i -*-■'- y-' ■" o "■ •■ i^ - • -'» - -. — .- ..wi..... fubtrahcndumcftet, ut vcra &ipfiCoeIo confona proveniret intcrcapecio,atque prorfus 'eadem,qua:exCentroInftrumentiprodircrficcntrumvifuscidemuniretUL.. Quavcre rationehac Tabula juxtaTrianguIorum planorumindudioncs concinnata fir, demon ftratur a nobis in Progymnafmatis Inftaurationis Aftronomica? volumimc noftroprimo pag.342.in capiteejufdemquarto;quodaliasapag,335.uf.]UCin 343. luculcntam hujusln- ftrumenti defcripcionem exhibeu, Ad quod ledorcm de hoc plura cognofcendi cupidum remitto EXPLICATIO FABRICAE eT VSVS. remitco. InvcnicccciamibidcmpauIopoflDiftanpasNovarftdlaravicinioribusCafsiopcc acqiuburdamaliisjtiimqyoqifixaniminccrfecxamrsimccodcmlnftrumcncomcnruracas' acqucinufumdcdudlas. Nullum cnim aliud huicoflficio accomodumcuncadmanusha bcbam : ucpocc nupcr e pcrcgrinacioncGermanica domum rcvcrfus , & Pyronomicis po- tiuscxcrciciisqiiam Aftronomicistuncoccupatus, Licecvcro hoclnftrumcncumnonadco £xcclIcnsfic,acqucca,quxpon:modum fuc- ccfsivis aliquocannis excogicavi, & magno laborcatque fumpcu confieri feci, idcoq; poftc. a mc anciquacum : camen illud qualccunquc fic, cum & ufui non incommodum cxi{lat,hic una cum ca:ccrisdclirtcandum cxporicndumq; duxi,qu6 & corum racioncm habcrcm,qui busopcrofailla 5c fumpcuofaadco Inllirumenta, conflrucndi non fuppetitficukas. liliacquc hoc contentire^lius&prarcifius, quamantchacpcr RadmmA- /Ironomicum fe rifc & cxpe- ditcpraecavcano. #i IN. aKggg^^^.^SLi.yg^jg^Sa!^ '*'^'^^?^:^C^4^^^o^^^i^-4^*i^ INSTRVMENTVM ElVSDEM VT ALTITUDIBUS CAPIENDI IN- fer viat difpofitio. EXPLIA EXPLICATIO FABKICAE ST VSFS. [NiTRUM£NTUM hoc ipfurti fi pracfcrcim ftxctncetn circuli capiac, cjus cir- cumfcrcntia,AlcudinibusquoqucSidcrUmrimanciis nontftinconvcniens ^mododifponacur/prouchxc appoficafiguracio oftcndic: t|ua ccjam raciono jcgo cunc ccmpori$,cum novaillaftella anno^i.&fcqucnCiconlpiccrccur, cjus Alcicudincm minimam , cum in Mcridiano infra Polum cfTcc, fcrucacu» f^^Tum : Maximam cnim quando vcrcici appropinquabac, dcmciri codcm non licuic, fiquidcm innoftroHorizbncc admirandacaftclla, cumfupraPoluminMcridiano cflcCjnonlongcZcnith di(Vicic:idcoq;incrafcxcam CircUliparccmcjus Alcicudocomprc- hendincquibac: quemadmodum fupradidolibro&codcm indicacocapiccharc&fimilia Vidcrclicco. Racio aucem, quaobfcrvacioncm inftitUcbam i ibidcm quoqucparcfaifla cjufccmodicrac: Scxcanshic>quoadRcgulam ABinfcriorcmin altaqUadamfcncftradif. pon cbacurfupra murum R,ica uc ptaccisc Mcridiano Coelcfti corrcfpondercc,quiobfcrVa- tio!ii adapcarccur^. Eratq; fulcrum quoddam liccris VX indicacum huic fuppoficum; idq; apartcpoftcriorivcrfusCcncrum juxcaT, cjus fublimicatisuc ipfaRcgula A Bcxaftccum KorizOnti$a;quilibrioconvcnirct: Idq; hocmodocxplorabam: Arcumlnflrumcnci KN cuinfuis rcgulis ad meridijini planum dirigcbam,5c infincubi cfo. Gradui dcfinuhr, jUxcjL^ N appcndcbam pcrpcndiculumpcr N S fignacum, aci-cgulam fundamencalcm A B pcr cu . ric js quoidam intra T & V X, poficos ♦ prouc opus crat, accollcbam vcl deprimcbam ; unaq; fi curiiverfumInfi:rumcncum,donecfiiumOrichalcicum NOS cuiplumbum juxta S an- heclirur , prjccise puntf^um mcdmm incer Sexcancis CencrUm ad A , & pcriphcrciam divi- fioQisadOcontingcrct. LiQuctenimindc,quodOrganircgu!afivcba{is A Bcxai^e Hori- i2;onii acquidiftaric : Cum cx Elemcntis Gcomctrise fcxcans Circuli a Centro cofticuat Trian gulum ifolcclcs ( prout in libro quarto Euclidis Propofitiorici^, demnoO-racum cfl') per pun urrinq; divifioncs quacckim cranc adaptata: in parVo quodam Arcu PQ_circa cencrum N dcicripco ,ficutproquanCicaccGradusuniu$in calicirculidiamccro minucaabucraq;partcdifl:ribuerentur,inantcriori OPfubrrahcnda; inpofieriorc vcroO Qaddcnda,prout pcrpcndiculum hinC vcl inde aliquam ab equilibrio inclinacioncm mon ftrabac:Eoq;pado Alcicudinempcr ArcumBC invcncamobfcrvacioncpcra, ftibfcquenribus pagclli-. ibidcm rcferunruji,, Exquibus carum pru:cifio incclligsnci conft^^re porcfl", qux ccjar. cumiis,quxpofl:moduminDaniaaIii.sOrganis dcmtnfus fum apprimcconveniebanc. Ir ''Opcandum,uchcccximiamachinadiuciU3iri:hicconfrrTatafuiflcc,atqueufuiadhibica; vcl ccrccalia in cjus locum conftruifta... Scd cum homincs plurin^.iim ccr- reflribus rcbuspociusacccndanr, quam CalcAibu3,caliancgUgc- rc ioicnc, majorcforcc diipendio', quam ipfimcc fecile animadvercuau. QVADRANS MAXIMVS CHALI BEUS aUADRATO INCLUSUS, ET HorizontiAzimuthali chalybeo f ■ infiltens. EXPLI- EXPLICA1IO FABRICAE £T VSVS. TiIIn cquidcm QKadrancemrupcriusinrcr Inftrumcncadclincacamimcro^, jxplicuimus, aliatamenracione clirpoficum;ica ucintracrypcam muralem in ixcquodam forci ChalybcoZcnith &: NadirrcQ)icicntcconvoIuerccur,& imul incra muri crypcici circumferenciam, Armillam firmamhaberec Azi- muchaIem,qucmadmodum ifthic cumaliisrcquificis, huc pcrcincncibus, fuificitnccr & depittum &: cxplicacum efi-. Vcrum ciim ibidcm pollickus fim, rrie fuo loco alceram cjus dtfpoficioncm,qua ab inicio ufus fucram. oflcnfijrumjCn cam hichabcsrquiebrevibusficexplanabicur: A BCD ipfcQuadrans, ACcncrodcfcripcus, & Quadraco A E F.G comprehcnfusr'; Ejus Rcgula A C I , infcrius excendicur, ad manubrium H, propcquodcftpinnacidium, rimulashabcns fupcrioriadCParallcIasr'* Elongacur vc- ro aCinlfuperiore parce, uc Quadracum ubiq; contingcrcpofsic: cuifupcriusfilaquaedam Orichalcica juxca I fuficncaculi loco addita lun c,quod mdcx in linea rc6la ubiq; permaneac. Qua: a pofVeriore parcc vifuntiir A L Al N O fcrreum falcrum indicanc,Quadrancern cocum inplanoHorizoncaIifubn:raEoOrthogonaliterfufhnens^.Namjuxta AHorizontiAzimu^ thaliinftarccnaculihabcncisinfrafccochleolam pluniacam,afibciacur, ucin co pcr manu- bnum quod a poftcriore parce eft,m ipfo Azimurhali circulo quacunquc lubupriccircum- duciqueac. Ipfc vcro Azimurhalis Circulus, dcquoloqudr, per liceras P QR S rcprajfen- catur^. PcrXver6indicanturqumquc'coIumna; fortes tocammachinamgcfi:antes, apud quarum capitcUajuxtaYZ funtcochle3cqu;EQam,pcrenncsdi(fla:,cum fuis ccjam manu- briis volubilibus, Circulum Azimuthalcm, m a:quilibrium Horizoncis difponcnccs , & co- cum Quadrantem in vcrcicale planum dingeatcs, prour cxigunc perpcndiculaapud V & W fignaca:*. Cafteraconftantcxindicationcfatufupersuscitacoloco. Ubi hicidcmQua- dTansalitcr&aliquantocommodiusordinabatuji.. Non igicur lubuicpluradc hoccxpli- cacionis loco rcpeccrc, nc fafiidiosc cadcm, C[ux prius difta,rccoqucrcmJB»Uc verofpacium fubjeclum[nihiIominu$, vcluciancea, complerctur; Hexamecrum Carmcn addicum efl, quodNobilis & Dodlus Adolcfccns FRANCiscusGANiNFB Tengnagel, quiali- quandiu mihi fuicdomefticus, mca;q;cDaniamigracioniscomcs', quohicfubjungerccur, cx ccmporc concinnaviu. Edxtevos humiles Artes, cur/ta^(u^irjA Qeditc ; TSlam Mufcu tantumju^ra extulit cmnes tJr^inieDivinacapHtiCdefiiacitiantHm^ Gvuperant Terrasit^uantum lux alma tenehras ZJincit : Et os homini © e v s ip(e , ut Sidera ft?e6iet , Tam (ubUme dedit, ^uofurfum lamina icllatp ^etherafujficiat yfiormA vagaSiderafuhdet. Feiicesigitur, quthpt^hAcfunt EntheacurAy T)um c^uArunt ^ opes al/i, ^ feciantur honores, T>eliciasluxum^pe!unt ^ ludicraauAvis Tra£iantes , vnam /iupide pecorum injlar niertum ^raducunt viles. ^hcjuo ignorantiaCACa ^rkcipttes agit hos , cjuihtu hautfunt ardua cordi? . irucuifHensgenerofafuperni[eminisignt^ ^rdet y ih aAethereos alacris confcende recejfta. HucageTimdchareSfPtolemAeyCoperhicepCjuam^vii (fonjifinimiHm^ faUacthus /nftrumentis, liicet an rurrim liceat confcendere parvis i ^rAcelfamgradthtis , Coslofve apprendere conto? r Vl^ dextre qtiod disjun£lum & compo- ficumarcliore/patio &dire(fliorici{lul^, nimirumoblong ^Oy XXCIV, REGN/NTE IM DANIA FRIDERICO JECVNDO, HVNC 'COELESTI MACHINAE CONFORMEM GLOBVM, IN QVO AFHXA OCTAViE SPHERiE ^IDERA COELITVS ORGANIS DEPrEHENSA SV(S Qy/^Q.VE LoClS AD AMVSSIM REPRASEN» YaRE: ERKANTIVMdVE STELLARVM PER RI^X APPARENTIAS PFRVESTIGARE DECREVIT: COELO TERaiGlNIS, QVI RATIONEM EAM CAPIVNT, M^CHANICO OPERE PATEFACTO, TyCHO 8RAHE O. F. SIBI ET POSTERIS F. F. Quodvcroannushicadlcribituri^S^.coid fic, qn«d iscirca medium tempus, dum haec ftruvfluraelaborarecur, incidcrcc; quadricnnio nimirum ancc cbitu laudatifsimae; memoriaeRcgis Friderici, quimcmeac^ftudialibcralitcr&clcmcntcrfovit, ac Rcgio Amore, quoad vixit, profecutus cft, Addam 3c hoc , quod magnifica haec machina fupcrius tcgumcn habet,per Y Z indicatum,in- tcrius concavum,arcp rotundum,quod fupcriiis Globi hemifphaerium compraehcndat,atcf in eo per funicula in cochlca trabi aflfixa ubi lubueritjdemifllim ipfum Globum i pulvcre, alqscp irjquinamcnci» prctcgat» Vfushuius Ctlobi eft,qualis(S«:aIiorumCccleftium: Quam peculiarilibroperotiumdefcribcrcanimuscfl, Ncq? cnim paucis abfolvi potcft* Habet aurcm prac cacteris hoc ob fuam magnitudinem praerogativar, quod omnia in co exa Aifsime ,adeoq? in ipfo rninuro cxcqui liccat; ficq; fingula,quae primi mobilis Dodri- ' nam conc£rnunr,& ccclcftium corporum obtervationcs rcfpctftu Ecclipticse dC AquatcriJ^ aliorumvequorumvisin Splixracirculorumminimo ncgotio, £c ablcj laborioj^a fuppurationc hic mapcba- nicc pcrficiuntur. iaiMaiiii DE IIS Oy^E n^ACTE-NVS IN ^STRONOMI. CIS DEI DONNO> EXANTtAVIMVS, QVACXVK, POSTHAC EODEM FAVENTE, EXEQ^VENDA RESTANT, NNO DominilJ^Oj^antcannoSjHimfrum^f.quo tfxnporc con# june^io illamagna fupcrfommPIanctatumcircafincmGancriS^ initiumLco nis contigit , iuxta sctatis noftrsc annum decimum fcxtum complctum, Lipfiac li teris humanioribus opcram dabam ,fu{icntantemc ifthic una cum pardagogo, Patruo mco charifsimo GEORGIO BRAHE,qui antc annos circitcr ^o. . ___ fatisconccfsit^ParcnscnimipfcmcushonorandjcmcmoriaeOTTO BRAHE filios fuos jquos quincj habuit , quorum ego fum primogenitus , literis latinis imbui non adrno- dum cxpetsbat , cuius tHiueii «n.pfum ^^Ci pcer.ituit* Educsrst vsr 5 mc ab ipf ^. mf^,fnia di- dusPatruus^ajdcinccpsliberaliteraluitquoadvixitjufcpinaftatismcac annum dccimum ocfia- vum,fcmpcrcg ixlii loco habuit , at<^ in haercdem adoptarc conftituerat» Erat cnim iplius coniu giumftcrilcjin uxorcmdudia Nobilifsima QC prudcntifsima Domina I N G E R A OXONIA, magni illius PETRIOXONII pofteaKcgni Daniae Aulae IWiagiftri, forore,qu2e antequin- quenniumdiemcbijtjqux^meet,dum vixit,initar filijXmgulari amorecomplexacit.Haec poftea per duodecim anos in GynecaeoRcginaf,rcpore Rcgis FRl DERlCI \K laudatifsim^ mcmoriar, Aulaemagiftra fuit,fuccedeteilli ineodeofficiomatrcmeacharifsima ltaliac,GalIiac dC Germaniac - ficcp cum multishjncinde Illuftribus Qc Eruditis viris Familiaritcm per iiceris contraherc Iicetct,atq; mea in venta co latius in publicum ufum fjpargcrc* Pracfentiebam cnim, mc non fatis commode &: iiito hxc ftudia in Patria excolcre pofi!c,pracfcrtim fi inScania,arcu fede mea Knadtftorpiana,autahtiin amplaqua dam Dani^ pacrtc hacrcrem, ubi Nobilium & Amicorumcrebcr efiTet concurfus , qui talibus,otiij Philofophicum intcrrumpcndo,impcdiamefOcftent, Vermumcnimyerd accidit,utdum harcani mo fccreto volucrem,iamqi me itincri tanquam id non agens,accingcrem«Scrcnifsimus dC Potcn- tifsimus Rex Daniac dC Norvvegiae Fridericus Secundus.laudatifs» memoriac, unum cx Nobilib» fuis pucris Knudtifiorpium ad me cum littcris Regtjs mittcrct,quac, ut fe confeftim accedcrem, u» bicunc^ fn Ze[andiarepcriretur,iubebant. poftquam igitur adutum comparuifTcm, optimus ille,& nunquaran fatislaudatusRex,fpontetama?diriciaquam inftrumcnta varia Aftronomicaobfcirvarionibusaccurateinftituendis idonca abfolvi, quorum prxcipua pars hoc libro dcfignata, dC cxplicara eft. Interca etiam obfcrvationibus ftrcnue in vigilabam , accitis in harum miniftcriu pluribus ftudiofis acumine ingentj dC vifus pollentibus, quos alios illic continue luftcntavi', ac hifce Difciplinis dC pluribus aliis Philofophicis inftruxi, Sicc^ Dci benignitatcfa {lu eft ut nulla fcrmc fcrcnitate practcrmifTa , plurimas, casc^ cxacf^ifttmas obfervatiohcs ccfclcftcs Aftronomicas adepti fimus j idq^ tam in fixis ftcllis,quim omnibus Erraticis tum quoc^Cometis interea cluccfccntibus, quos fcptcnos ifthic Cochtusaccurate dcnotavimus* PcracfJac autcm funt hacrationcibix; annorum fcdulac oblcrvationcs^quasprimQinmagnisvoluminibusconfcriptas poft^a fcorfim infingulos libfos, pro quohbetnimirumannodiftribuid^admundumdefcribi cu ravi : idcj^ tali ordinatione pcrcgi,ut ftellac fixc fcorfim quodquod illo anno deno ■iih-.mI i nos m paulo adhuc mcHnatioreSph3rra,inc^f nfula udic^ mari tnagis vaporofocmda^cu multotic | ('Ui dic^um) confpcxerimas ^atqjdemenfiOmus, Sed forteaedcs habicationis Copernicierant ita dirporic2r,uthbcrumundiquacppraebercntHorizontem,ldeoc^minasobfervationibus,praelertim eiufcemodi dcclivioribus commodac cflTcnt. Quod dC retulit mihe Studiofus ille meus,qucm ante annos } ^, eo. altitudinis Poli examinandac caulsa ablegaram» Quocirca Copernicu5|)ropriis in Mcrcuriodcnotationicusdeftitutus,nonnulIascxlibroObfervationuGuaIteri,difcipuIiRcgiO- montani, fi^^cuius Norimbcrgcnfis mutuari coacfius cft ; quashcetnon fatis fidchtcr dC praccise fuis placitisatcp Demonftrationibus applicuerit^ tamcn optandum forct, utinreliquisPlanetis, quos cx fuis obfervationibus rcftitucre ingenti aufu laboravit,non multo incertiores obtinuifrer* Tunc ccrte Apogaca QC Exccntricitatcscorir, reliqua^ hucconduccntia longe emendatiora nunc haberemut : cgocp multorum annorum maximis dC indefeflTislaboribus fumptibuscp ingcntibus parcere potuiflem, Quarecum z ) annorum felccf^ifsimas dC accuratifsimas obfarvationcs variis j ctatfabreeiaboratisi Orgaiiis, quat i ii anictedetibus oitenuimu3,Coelicusconquiiitas in promptu j babeam , ( ut nihil nunc de j^, antccedcntim annorum annimadverfionibus dicam ) eas rarifsimi dC prctiofilTimt thefauri loco cuftodio : quas tamen cuncf^as aliquando forte publici iuris faciam, ubi adhuc plures iis adiungere, Divina concciTerit clementia. Exquibus omnibus liquct,meindca demicofcxtoajtatisanno,Sidcriumobfervationibus adfucbus adfuevifte ; eascp per annos penc continuos Jf » hucufc^ continuaftetinter quas aliac tamc funtalrjs certiorcs fin: pracitantiorcs, NamcasquasLipfis in pueritia,8^ulc^ adannumaetatis vi cefimum primum peregi,pucriles 8C dubitas appeliare foleo, Quas vero poftea ufcp in vicefimum ocf^avum annum adeptus fum , f uvenilcs dC mcdiocritcr fe habentcs voco, Tertias autcm, quas poftmodum Vraniburgi cxacfttiiTimisillis Inftrumentis in maturiore aetateperi)* ferme annos, ufcp inaetatiscompletum quinquagefimum maximademenfus fum,viriles,ratas,5(:ccrtifllimas ap- pelto QC cenfeo, Quibus etiam potilTimum Aftronomiae rcdintegrationem fundarc aicp exflruerc arduis conatibus cnitor,licet5^nonnullac cx praeccdcntium annorum obfcrvationibushuc non pa- rum conducant,Quae vero in his ex Dei ope hacf^cnus Pracft itimus atcp claborata habemus ; quecp in pofterum ciufdemNuminis benencio cxequenda,pcrncicnda^ reitant,in hunc modu it habci: S O L I S ante omnia cx plurimum annorum accuratiiTimis obfcrvationibus reftituimus mo tum,non faltem AEquinocfiialibus ingreffibus accuratiftimd rimatis , fed dC locis his atq; Solftiti alibuspunc^is intcrmcdiis una adhicitis,pracfcrtimin BorealiOcclipticac femicirculo;fiquidem ibi rcfradlionibus Sol mcridianus non fit obnoxius, Idc^ utrin^ multotens conprobavi , atque hinc tam Apoaeum quam Excentricitatcm Solis hifce temporibus correfpondccia Gcomctrice de- duxi, in quorum utrocp cvidens crror tam Alphofinis quam Copernico irrepfit, adeo ut Apogxii Solis tcrnis proxim^ Ciradibu s Ccpcrniceos numeros antevcriar, dC Excentricitas fiti^ parc ium fcr^, qualium fcmidiameter Exccntrici 60^ Vbi-apud Copernicum pcn^ quarta pars unius defide fatur. In fimplicictiammotuSolisconftitucndo)hifec Annis quafiquartaparteuniusGradus crrorcm committit* Inde Alphonfiana cum Coperniccis coUata ar ftimari potcrunr^Dcduxi ve rohinctamacqualium motuum, quam Proftapheraefeon Canones numeris exadis:.utdcSolis curriculo ad amuffim vcrificato, numerisc^ idoneis patente , non amplius dubitandum fit. Atcj? 1 hoc ul in Sole omnium primo fieret,omnino ncceiTarium crat:fiquidcm is norma Cocleftium mo- tuum cxiftat, &' Ecchpticam , ad quamrcliquae motienes rcferuntur , defcribat» Cu/us ctiam ab AEquatorcobliquitatem maximam aliam deprehendi,.quam Copernicus&eius coartanci,utpotc part : 2;. Min ! 3 1 5. idcQC^ 5 ^ minutis illorum in vcntionc maprem, prxcavendo nimirum refra cflioncm Solis inBrumali Utu , quam illi inconfideratdneglexcrunr. Providimus etiam Soli pecu- liaribus Rcvolutionum canonibus : tum quocp Declinationum& Afccnfionum Rearum novos canones noftris inventis fundatos addidimus, Qain&: Parallaxibus, dC rcfradiionibus eius Ta- bdlis fingularibus conluluimus, In L VN A ctiam non minorem adhibuimus diligcntiam, uteius erroresfaIvarcntur,qui multifaria pcrplexitate involvuntur,nec adeo fimplices func aut tam facile paiet, tit vctcrcs,&: Co pernicus cxiftimarunt* Nam ft^aliam quandam habet ea inxqualitatis infinuationcm fecundum Longitudinem,quam ab iis animadverfum eft.Ncc ctiam proportiones Circuituum fatis prxcisc inea dcnotarunt. Quin&Latitudinis maximac aliosiila exhibct limites,quama Ptolemxoprx finitum,qnemhacinpartenimisfecureomncsoGeteri Aftronomi pofteafecuti funt:imo&:hanc j ipUm iascqualitcr mutat Luna ad diffcrcntiam tertiac partis unius Gradus. Nec etiam uodos eos, f ubi Ecclipticam eius via tranfit,arquali motui,ubi hactcnus exjftimatum,fubijcit,fed fingulis revo j lutionibushincindc nutarcfacit, idqucfenfibihdifcrimine quod a qualibct parte (cfquialterum I Gradumnonnihilexccdit. Quemadmodumhxc omniaexj6, annorum diligentiirimisobfcr-l vationibus dC animadvcrtimus QC rcftituimus : intcr quas ;8. funt Lunares Ecclipfes,accurate Coe- litus denotat«,Nec^ cnim ccruac fufficiunt ad primam eius inacqualitatcm fcrutandam^veluti Pto iemaeus ,*- lemxus, Albatcgnius, 5(^Coperhicusopinabantur) Adhibitareti3 funt in conOlium fex Ecclipfa tiones folares, quatcnus ear huc quidpiam ccnducerent» Et prar terea Luna in quadraturis, &^maxi mis elongationibuj a medio motu tam circa Apogacum quam Perigarum , locaq^ intcrmedia mul tifariam dC fjepiflime explorata ; ut intricatus eius motus rite conftarc poffet : Qai nos muUorum annorumincredibililaborctorfit» Adinvenimustamen demumrationes,quibuseiusin(labilcs& multiformesdtvagationes Circuiis3«^Numeris parerct.ldeocp S^conftitutc^ alia 6^apparctiis con- fonaHypothefi,Numerostamxqualiumquam ina^qualiiimotum, non folum inlongitudinc,fed fi«^latitudineadaptavimus,5(^ParallaxibuseiusaliterjquamaPto!ema!o6;:Copcrnicofa(fhtaiitefi:, PrOut experientia ipfi una Hypof hefi confentiens requirebat profpcximus: nec ctiam rcfradtionu Lunarium curam omifimus, cum fine his cajtera non exacfle dignofcantur» Quae omniad'nonnula alia Lunares apparentias concernentia, in Canoncs fuccincftos redada, caiculo,motibuseius inde crucndis deftinuavimus, Quare fic reftituto utriuscp Luminaris curiculo , ut ipfis apparcntis Ca* leftibus corrcfpondeatjtam Hcclipfes erunde quam cseterae configiirationes , mcdus atc^ ingrcftus pofthac rccftifsime conftarc potcrinc : qiiod hadcnus diu defideratii cft, Qii^ vero hucuf^ dc So lisSs^ Lunx.quoad motus eroru Caleftibus annalogos, rcftitutioncdicla Innt, ea &:his Piura, ca- putPrimumProgymnafmatunoftroruuj Aftronomicx inftaurationisluculcntcr cxpedict* Ibi horum cupidus voti compos reddetur. Reftat rolummodo in LuminarD horum ulteriorc confide- ratione, ut omnia pluribus feculis adaptentur, d>C univcrfaliora rcddanfur , quodiion adeo magno negotio prajftari poterir, quatenus veterum QC antcceflTorum obfervationes,quibns inniti oportet, ritefchabent. HancveroplenioremS^CathoIicam expofitioneminopusTheatri Aftronomici refcrvamus» Interim Aftronomi»^ addid}us iisque inProgymnafmatis Gicatolocotradidimus,ad- modumutilitcrfrui poteric, dC fuo fatis facerc defiderio- Prar lerea S T E L L AS INERRANTES fivc fixat omncs,quodquod vifui utcuncp patet, adco^etiam cas, quae fextae appellantur magnitudinis, intcrimetiaaccurariffimc verificavimus tam fecundum longitudincmquamlatitudineminipfo minuto •adcoqpnonnuquamciusfcmifire: Suntcp hocmodo millenac a nobis recflificatc ftella: , cum vetereS non nifi 2. z, pluresnumcrarint, qui in rciftorc Sphacra habitantes.ultra 200, cerncrc poterat,qtix nobis hic fempcr latent: in quarii tamcn locum nosaliasminutulasrcftituirausab rjsob parvitatempractcrmilTaJr Laboravimns in hoc arduoopercpcneio Annis,eo,qjvarijs Inftruitjetisrcmomnemaccuratcexperiri vcluimus, Quia vero minutulac Stellae non nifi hyemc cum obfcura: funt nocles,£Llatcnte :unc infupcr Luna cernuntur.Ideo multoru Annorum requirebatur expe(flatio,antequatn hafcdebicc dC fufticicnrer abfolvi poftent; cum etiam circa ipfa novilunia,quando ha:c poiilT(mum,praxi fub/iccre Oporteat raro fucrit fcrenum.Quavcro ratione per Venercm cam Eoamquam verp^^rtinatii jntermediantc Solc in iixaru quoad longitudincs ab AEquinodio,exa(f^um cognitionem pervcneri*mus5i.'mul' tifariam id ipfum comprobavcrimus , rcvocatis omnibus ad cam qiix lucidior eft fupra capuc y nu- mcrOtertia(quamdataoperapro fundamentoreliqiiarumconftituimus^cumduaranteriorcsmi' nuspateaiH)caput fecundumdidiorum Piogymnalmatum abundeexpediet^vnacpquarationc alias hinc deduxerimus ; dC primc, quomodo triplici ratio per totum Cotli ambitum iuxta Zodia- Cuiii ^ ACquaiCrcAi iLl«;:c»iorcs quaiuati^tin iCiiuS vcrcrcs lecundum Epicydos cxcusarunt,variationicuidamobnoxiume{repcrfpcximu^:Q.ujbusomnibus,atq5caetcrishucpcr- tincntibus pecuhariquadamHypothcfianobisantc;^» Annoscxipfis apparcniiisadinvcnta&: conftituta confuluimus,quam ali| quidam, intcr quos n cs notabiles lcio, pcitea pro fua invcntionc fibi arrogarc,&: aliis venditare nimis pcrfricfta fronre non crubucrunt : veluti fuo tcmpore dC loco V. D. occafiones horum indicabo,atcp corum nimiam hceniiam rcprimam &C rcdarguam, itacj? fe habcrcadeo evidenter convincam, ut non fit finccro iudicio praeditis hacfitandi aut contradiccndi locus. Parcam vcro iis fi ingenue admiftum faflTi fuerint,5;: mihi mea rcftituerinu Ideoc^ a norai- nandis illis nunc volcns abftinco» Latitudines quoc^ Planetarum incmcndatas , prout praedcccfforcs noftri indc A Ptolcmaco,non permifimus, fcd »js in quinc^etiam Planetis diligcntcr pcr totum Circuitum atfcndentcs,alimetas aliosquc per Ecchpticam tranfitus definivimus.ut omnia ipfi Calo ccngrua fint : in quibiis in cvi- dcnter animadvertimus , trium luperiorum Pianctarum nodos , iivc limitcs maximarum latitudi- num , Apogaeorum motui non cffe,conformitcr obnoxios , fcd alium obtincre pcr fc proprium, fi modoca quae a Ptolcmaeodchis tradita funt recfle fchabent , aquo tam Aiphonfinic]uamCopcr- nicus fuamuiuati iunt, ncc ullam cx Obfervationibus proprirsccrrCvftioncm adhibucrunt. Vndc Ht , ut Pianeta: nonunquam in Calo fint Auftrales , cum corum numcri rllos Borealcs exhibeant, atcpecontra, Rcftat igiturnihilaliudinquinc^crrantibus Stcllisparitercxantlandum,quamut hacc,quar circaLongitudinesS^ Latitudincs,atc^ omnia hucpertincntiaaliter fc habere.quam fcruntufitacac Tabular, jam uitra if ♦ Annos (ut dc ;o, prioribus nunc laccam^coehtus dedudis accuratis Obler- vationibus vationibus cxplorataS^conftituta habemus, in novoiSi^ compctcntes Canones rcdacfl^anumcris ex ponantur, quorum etiam quacdam initia dC fundamenta jitn a nobis f ada funr» Csctcra per aliquot calculatorcs non difiiculcer complcri pocennt , 8C poftea fcqucntium Annorum , quorquot lobueritjEphemeridcshinccxpangi. ldemq^inSoleS«: Luua,quorumTabulasiam in promptu I j| habemus, praeftari,quo ficfuturis temporibus minimonegotio procari pofsit . motus Corpotum| Coeleftium a nobis rcftitutos ipfis apparcntijs congruerc Sk^ undiquaqj rcC fruftraneanonfolum vulgb, fcd 6^ plerilcp Do(Seius cauffa totum te viderc] venerarb & amplcxarinon minus avide concupivi, quam illi olim^qui cx ultimis H«fpa# | niae finibus ad Livium videndum in urbem profe<^i funt^ Auxit hoc meum dcfidcrium humanifsimahapc tua conpclIatio3& in tantum auxit,ut nifi Caefaris voluntas; & munc» ris publici ,quod gcro,ratio prohibcrent : itamc D E V Samct,ncque itineris intcrcapcr do&molcftia nequefuavifsimae coniugis dulcifsimorumquepignorum amor&illeccbrae me cohibcrcnt, quin arrepto itineris comitc communi amico Thaddaeo Hageccio ad tc in Daniam ufquc cxcurrerem, Dicerc ncquco, quantopere me dcicflct cum Hagcccio, mente poftquam corpore non poffumus^totam Hucnam perluftrarc>&inprimis cxa£l:if' fima tua obfcr vatoria Inftrunicnta,totum deniquc Mathematicum illum apparatam vel maginatione tantum complcdli. Quid vcro Ci ipfc fpcftator adcflrem,tcquc ipfum om* nia non cxplicantcm tantum, fcd cxercCntcm viderc polTcmf Scd id quia optare quidcm icet , fpcrarc hoc temporc vix ( nequccnim omncm fpem penitus abieci :)miffum iam ciam,<& ad Epiftolam ruam converfus , paucis ad fumma ciuscapita rcfpondebo, At^j^ hoc inprimis* Quod iudicum mcum de fcriptis tuis amanter exquiris > quod ccnfurae meap, cam quae tibi cum doclifimis quibufdam viris non tam lis quam amica cft conccrta tic fabfjcjs, ;n eo tantum mihi i tc hoiicris tribuiaccipio, quaiUi iioii faLCiein,fi Ivcgcs &Principcs de Regonis & Provincfjs integris dcfccptantcsj mc fibi ludiccm conftituc rCnt. Vt vero,id quod petis & offers,mihi facicndum fumam,ncc cruditio^qua? in mc aut nulla eft,aut vere exigua,ne^ modeftia mca patitur» Ne tamcn ad tam amicam poftula tioncm plane furdus fim, hoc habcto. Dc fcriptis tuis quid in gcnere fentiam , tcftabitur Capfareae Maicftatis privilegium;,quod hifcc literis adiun^flum ribi mitto , cuius ita fcri;> bendi cgo Cxfari author,ct porro,vcrain eo C3C,farcm teftari, fponfor fui. In fpccic vc# ro eaquae deComctis pofterionbu$^quotquotipfaobfervafti>atctraditafolidtfsimis^ rarionibus confirmata funt,taliacffe puto,vtdei}s nc ambigi quidcm amplius ab Erudi# tis viris qucat* l tacp non adducor,ut credam cos qui hac in partc dubios fcfe adhuc oftc« dunt,& contra demonftratam vcriratem Ariftotclis authoritati pathrocinari videri vo*. Iunt,id ita vere fcntire.Scdhoc potius,eos agere puto,ut,cum omnem movcrint lapidci omnia^ip undicp conquifiverint,quaeAriftotelam fentcntiamconfirmare tuam vero Iabe# fa(^arc.,autdubiam reddere videantur,eatibiproponant, tanquamat Lydium lapidem cxamfnandaadeoq^cauffarntibiprafbeantjCruditionistuaeSolc, omncsomninocrro* rum tcnebras non modo , fed vcl lcvifsimas nubecuias dlfsipandi , cxaflifsimamquc harum rerum dodrinam^poftcritatipcrficictidi ♦ Qj:}^ fi hac mentc tccum ccrtant^nae cgo j ' illis iliis qisart^ maxirt^e bd^ccupio, ifinaliua agiint , pcttinaciam quidem coru cfdio dignattt «xiftimoildtamenquodpcrtfnaciafuain communc bcneficium tibi extorfcrunt , ipfis vaidrc, vel potius non valcrc iufsis ampledor non fccus.ac fi bona id mcntc fcciffent^ dk c6(^ rcipablicac litcrariae gratulor. Dc priorib, Comctis,quos Rcgiomontanus & alq obfcrvaVunt^expcfto qu^ propb dicm cditurus cs^co ufq^ mcam quocp fcntcntiam,an in vni vcrfum omncs Comct^ a?thi^ m credcndi fint , an vcro pars clcmcntarcs^fufpcnfurus* Ad ca^quar no vis tuis hypothcfiKhaffcnus obicfta funt, folidc mihi vidcris rcfpodif fc neq!egoquicquainf)sabfurdum,fedomnia inviccm pulchcrrimc congruentiainvc» r.io:?.n vero hypotheffs ifty^id ^io Copernicianis defideratur.praefiiturar fint>vtfcili# ccf cxa£la Sidcrum loca ad praeterita prarfentia,omnib* omnino InftrumentiSiprartcrea qua^ad voluptatcm tantum compara tur,careo,Quadrans Nonnianus multiim aliqiiando mc habuit foUicitumtfed quia difii# cilhme imo ferc impofsibilc cft cum coficcrccogitavi ego dc alr)s medf)s>& inveni varia, quoru partc Chriftophorus Clavjus infignisMathematicus inlibcllo fuo dchordlooiis f^larib.pcr Inftrumentij dcrcribcdi>cdidit.Tahdc in mcntc mitii vcnit quadratii» tiiiufda conftruclio^quac quiajdo£lis quibufdam viris no inclegans vifaefi>voIuicamad tequo^ mittcre* Vt tamen ingenuc fetcar quod res eft.quod6|p vcnTsimcaffirmas : ihvcntiones haf omhes mihus habcnt in receflTu , quam dc fc prima frohte fpondent; Gratum ta« mcn mihi crir tuum de hoc uldmo mco invcnto audirc iudfcium « Ex N* N# Pligiarfi tui libcllo» qucm fundamcntum Aftrdnomicum infcripfit, Unicoqut dus diagram« matc. idHMitoMiMlNH |w.~*- ^..^/4 D«»ifl/n V/V^tVfVlnir» ^<»rliV«»y«f mnG^rtfvi «»nrr% nryfi? riifi c nliehiis.ClJm on 3dl/er« I Cam valetudtnem publieisflcgo tfjs vacarciionpo(Tcm,novamf^^ itum do^rinamiinijuapcrtabulam finuum,tangcntium,& fccantium omncs tam rcftan* Igulorum quam obliquangulorum caAis.finc vlla multiplicationc vcl divifionc pcr fola I additionem & Jubtraftioncm facillime perficiuntur. Eam quoquc ad tc mittcrcm, nifi ircircm tt rcmtotam/oloco diagrammatcinfpcdlofacile arfccuturum. Exillocnim diagrammatc & axiomatc a multis iam dcmonftrato,quod radius fit mcdius proportio* nalis inter finum rc^lum arcus & fccantcm complcmcnti, to ta ca rationc cxtruda cfi:. Quod rcliquum cft , vakre tc itcrum atc^ itcrum, vir Nobilifsimc, in multos annosprc# <:or,& omnia.qu» a mc in tc proficifci officia amoris & bcncvolcntiar porrunt, tibi pcr# amanter affero,cnixc rogans.quod ultro facerecaepiiii , me tc cx animo amantcm amare pergas^ Datae Pragae Sg.lunf]* Anno qo^ lacohusCurtiusdScn^tcnauu^ QuU vfTo QuidrdntUyCUyMin tkerU mentionmf^icit^defcriptio adjtmaafuit: lubct er hctnc apponerc tflquidem in^cniofa (it.cT ahji ejitfcemodi tm i Nomino ({ulm cteteru produ^is mventionibus pr^valet : uttamen . ut C7 i>/c Dominui CurtiM ingenuc fatetur , non habent ejufcemod'. [ubtilitates in permiore recefju, <{md primdfronte ^Qlliun* tur : \nquibmfubfcnbit tjs, quthac de re Tomo jecundo Progymnafmatum parte priorepag, 4.^1. de codem Nf^o. tio a(]eruntur,Sumpr£[erquhn,^uodintricateh£t:s-iaboriof£fubdivi{iones,aliquid Utenns vitij nonnunquam fa- xAe infimtent .'admictitur gt hoc incommodi , i^ttod quidam Qj^adrantes, qu6 centro fumpfopr iores.co r>inores eu» dunt, Ideoque fubdivifionum mimis capaces , f^ ipla Kcgula.finon exaHillmc Unem reaxm ubique , qu^ tranfit, exkbeat.pundumq; aliquod in mcdio fcindat, (quod difficulterdignofcitur) fruflrd hU laboratus : vf alids incommodiu Utesnuttcpr£tcrcam. Qu<^renoflr4 ratio,quxpropetpfumlimbum<:irQuadrantis circuntfcrenttxm fit ,nec muUum occupat ^atij, v fucileetiampararipote(iMnge€(icxpedttiorcr certtor; cametiamperfe , qune quae poftea defcribendae funt partcs,cum prio ribus confundantur. A tcrmino huius primae partis transfcratur in quadrantcm eius fcmidiametcr,&arcus, quem is fubtendis^dividatur in fcxaginta partes arquales, critep quaevis harum partium gradus unus aut minuta fcxaginta, femidiamcter cnim cuiufvis circuli fubtcndit fextam partcmdrculi.hoccft^gradusfexagtnta, Dcindcatcrminohuiusarcustransfcruntur in rcliquum quadrantis,harum partium viginti oao,erunt6p partes aequalcs,quarum fin^ j guUs gradttm unam contincrc diximus oifloginta oflo , (Jufbus fi addidens primam illa| Jpartem.quam oftcndimus contineregradum untim & minutum unum^ cxurgent.gradus o accipiatur arcus graduum fe^caginta duorum^dividaturqp in partcs fexaginta sequalcs^aut arcus graduum trigtnta & unius di^ vidaturintrigintapartesafqualcS;CtcontincbitcjuKuis harumpartium gradum unum & minuta duo. Harum quoqp partium non nifi prtnia utimur, omifsis reliquis. Ex tcr* mino vcro huius primae partis transfcratur itcf ura in quadrantcm cius fcmidiamctcr,diui daturcparcu5,qucmis fubtendit,infcxagintapartcsaequalc$,&carumviginti o£lo pfo# feraniur in reliquum qasdranrisjhiibcbimufqacitcrum odoginta odo gradus integrcs : j quibus fi primam partcm^qusc gradum unum & duo minuta continct,addidcrimuS;,cxur gct arcus graduum ofloginta novem & minutorum duorum, critqp ultima illa pars,qu2e ufcpad finem quadrantis fupercft,minutorum,quinquagint3 odo. Pro tcrtio quadrantc accipicmus ab initio arcum graduum fexaginta trium^di videmusquc cum in partcs fexa? ginta arquales^aut dimidium cius in triginta partcs acquales^& acccptaindeprima partc^ Omifsis rcliquis^contincbit ca gradum unum & minuta tria. C^^^^^ pcragcmus non fc^ cus > ac in primo & fecundo quadrantc faflum efi« Proquarto quadrantaaccipicndus cDiarcus fcxaginta quatuor graduum,pro quinto arcus graduum fcxaginta quincp , & ita pcrgcndum,accipicnduf^ fcmpcr cft pro qua* I drantc fcquentiarcus uno gradu maior,ufc]p ad quadrantcm quinquagefimum nonum, pre quo alTumcndus cft arcus graduum ccntum Si novcndccim,dividcndufc:p, vt prius, in fcxaginta partcs sequalcs^auC arcus graduum quinquiginta cum dimtdio, dividcdus cftin triginta partcs2cqualcs,continebitq^quaevis harum partium gradum unum , & minuta quinquaginta no vcm» A tcrmino primar huius partis omifsis rcliquis,transfc* rcnduscftitcruminquadrantemciusfcmidiamctcr^&arcus ab co fubtcnfus dividen^ dus in partcs fexaginta arqualcs^earumqp viginti o<^o profcrcndae in reliquum quadra* tiSjhabcbimufcp iterum odoginta ofto gradus integros^quibus addita prima illa paric, cxurgcntgradus o£^oginta novcm <& minutaquinquaginta novcm , & proindc reliqua pars,qu2C ad finem ufcp quadrantis fupcr cft^ continebit minutum unum# Hac ratione divifis ifiis quadrantibus^adfcribatur primo quadTanti,qucm in nonaginta ^qualcs par^? tcs divifimus* o» In quamcuncp enim partcm cius quadrantis lineafiducif inciderit,cQn# tinebit arcus is gradus intcgros pr^cifc<& nihil ultcrius«Proximo,qui huc fcquitur, qua* dranti, adfcribatur* |«. In quamcuncp cnim partcm huius quadrantis fiduci^ linea ortcn. fos^minutum unum.Sequenti quadratiadfcribatiirz»<&hLicproxim?fcquenti5»poft4. <&itaprogr«diemur ufcp ad iatimum quadrantcm,cuiadfcnbcnda funt ^9* Qj^^^ «n quamcuncppartiumhuiusintimiquadrantisfiducif lincaincidcrit, contincbit arcus is vitra intcgros gradus minuta quinquaginta novcm» Exhibet hic quadrans adu & rcalitcr,partcs quinquicsmillc & quadringcntas,omnia fcilicet prima fcrupula quae in nonaginta gradibus comprchcnduntur, vfus autcm pcrfa;; cilis eft^Cadentc fiducig line^Jaut filio perpcndiculi,in partcm aliquam integram alicuius cx his quadrantibus adrjciantur fcmper gradibus intcgris : quos fiduci^ linea vcl pcrpc* diculi filiuai , oiiendit, tot minuta , quod adf^ripta funt ei quadranti a latcrc , <& prodi* bitnumcrusgraduumcarum,qucmadmoduatccmcndatae funt , utmihi ufui cffe pofsit^in mcis brcvi ad prar lum rcvocandisEphacmcridibus/ad hacc notitiam aliqua Eccentricita tum Planctarum, itcmquc commcnfurationum uniufcuiufquc corum orbis, fi eas a Gopcrruanis difFcrrc invcniiti,ac corrcxiil:i^ Qif^d fi cnihigratificari non dcdig^ nabcris.cfTiciam profcdo ut tc non pccnitcat bcncficr) in mc tuitNamquc ca qu2t huma ♦ nos &iibcraliumartium Profcfforcsdccct, /ng€nutafC> tuarumtcrcruau3orc,1audar< in mcis fcriptis mihi conftitutum cfi^, Meum vero fenfum ac iudicium, dc tuo illo prafcla^ ro laborc,circaGomctamanno)f77.corpe£lum,nc dcfidcrcs;Sichabcto^ vir Clarifrime, Cum cnim incrcdibilcm in illo dihgcntian tuam & accuratam oblcrvandi viam pcrfpcxc^ rim , m«hipcrfuadco,forc, utcoelci-iiumcorporum motuscmcndarccxa£lifsimcpofsisj iruduquc opcra? iilius maximo omnium l^udio , atquc cxpcflationi cumuiattfstmc fatis^s iacias, undc nomini tuo fcmpitcrnum dccus adtungatur. Cupcrc tamcn,tcin motu Mar* tis obfervando&cxaminado maximc incumbcrc , cum cum obfcrvari non poflc cxa^flc ? vu!go pcrfuafum fit: atiq^ cgo in ca fum haprcfi ut puic immutari Ecccntricitatcm ipfius penodumquc fua haberc, ita utalia in co introduccnda fit dtc^iiztio Ecccntricitatis :aHo* qui fit tabula cfficiaturpro maxima Ecccntriciratc, non poteritmtnimaf infcrvirc, «- iifmmmmmmmmm^mmammimmi^mmfmmmmmmmmmmmmm Subjun^U erant buic EpifioU qutdam pmjiantium virorum apud Ualos Caminai Wter (jud hd c ExceUcnti^imi iUiua Andr* Chiocci addere locus patitur, i^dNol)lIij?imum,acDo^tj?imuminrum TYCHONEM BRAHE VRANIBVRGI fundatorcm,& Aftronomiae inRauratorcm^ i\p^^^^^^ VM rapidos Co:lorum orhes^errantiap OiK^oti/ Tt/ittjb'Oj 7tO|uia AayToc p«f up : Mo^vop i7rf'» Tou Av7ou» Qjw ddhuc aliqtiid fupere^ fpatij qut fequuntur, patt(uU,ftc expetente Typographo, fubjinigipfrmifj, ex Uteris c:jnfdam tAcdtcin^ Doctoris Patav.j commorantis ad pucndm jliidiofaia Dammante fexcnnium duiis, excerpta* AGiNvspcrtotamfcrmcxflatcm HicPatavii <& Venetiis mora* tus cft* Qja dc cauffa, non fatisconftat» IntcreaG ALLiLEvsdcGALLiLAiis FloPvENTinvs Profcf«io* ncm Mathcmaticam hic adcptus cft , qui fuarum Ic£^ionum fcptimo Dc* ccmbris initium fccit^ Exordium crat fpkndidum in magna auditorum frcqucntia#A Dno.PiNELLo isIibcralitcrcommcdatunquCjfiporTcr, pcrlibcntcrin Dni T Y c H o N I s amicitiam infinuarct. Tujqui animum T y c h o n i s novifti j potcris , quod cx rc cr!t,in hifcc difponcrc* M a g i n v s cdidit nupcr librum 5 cui Titulum fccit rTabulaTctragonicajfubTYCHONispatrocinio» Excmplar mibi ad tc mittcndum deditquodprimaoccafionc tranfmittam. Rctulit ctiam> Illuilrifsimos V enetos in confilio rogatorum dcliberafre, utaliquis Matthcfci^s peritus fiipendio ^oo» Corona* . , torum in ai G Y p T v ai ablcgarctu,f,qui pro T i c h o i^i e iilliii: obfervarcr» Tantae cnimWcTYCHoccrtecltccIcbritatis>qu3nt2cnemo corumjqui nunc vivunt. Data? Fatavrj 2$. Dcccmbris Anni jf^z. Ex X t]uo itacpc pra-mifsis Clarifsimi illius M AGInilitteris inteliigam^cf^ lcjn italia Magn:fi :os quoldam & praeccllcntcs viros,qui Aftronoajicis ^ J^^^ rebus addifti, OrganactiamadnoftrorumiWtationcmp2rare,at6pob;; Sj^^Wl ^'^*'V3tioncs Corporum Coclcftium his fubtiliter perficerc non intcrmit* g^%^^^^ tcndum ducant^cfifaneidmihiaudituquam iucundifsimum^Nccdubito quin eximia utilitas ad Artcm Aftronomicamampliandam hincpromanarcqueat : fiqui* dcm inrcifliorequamnos, habitentSph3cra,<& folcrtiaprarditifintinfigni^opibusqpin^ fupcr va!cant,quibus hofcc fumptus facilc fuftincant.Optarcm vero ca qua? hailcnus ab ilIisCalitusdcprehenfafunt,mccLimaturecommunicari>quodnunc commodiusficri poiTc exifiimo , fiquidem in Germania degam at6p hoc temporc prope H A M B V R- G V M , Emporium cclebrc, quod cum ltalf'3 quoqp plurima habet commcrcia;, in Arcc quadam RANZOVlANA fubfillam: aut ctiam^fi alibifortcpofihac in Tcutho* nia fuerim , id quicquid crit facile me inveniat. Potinfimu vcro id quod lUurtrirTimi V E N E Tiarum Magnatcs Cuticx Iitcrif,qu3* rummodomentioncmaIiqualemfcci,percepi)antc paucosAnnos Heroico nrcj^lociis pa^iatu*"» H^r c au^c «n A I KX^ ANDria pra?cipuefa£litandaexpcriundacyccnrercm, quodquammaximccrcdibilcfit, PTOLEmaf um principalem \n Afironomicis Artificem,Ioc! eius in quo vixitlatitudt' ncm^, fcu^ quod idcm cfi Poh fublimitatim quam cxai^ilTjmeolim nimirum ante qufndc cirncircitcrfaeculademenfum fujfle : itautunius veialtcrnisfcrupuli nonlatcatcrror^ quin3>2»Gradusdcficientibus folummodp duobus Minutis ea adimpleat : quod & qui» damcxcius antecelToribus adinvcnerunt» Nam quapdcalfjs Poli vel iSlquatpris inchna;^ tionibus, ab ipfo in Geographicis, vel etiam alibi ab literis referuntur,fidc cxafla carentt & ut plurimum fecundum arltimationem lato njodo fumpta funt : quemadmodum & in affixis Sideribus, qua? in uno aliquo Honsonte pro maiore partc fingulis Annis vifurt* tur & obfcrvari pofiunt, non cajqu^c rcquirebatur, fecundum longitudinis & Iatitudini$ dimenfione adhibita efi diligentia^Multo 'gitur facilior lapfus contingcrc potuit \n Tcr^ rcni Orbis locis non ita patcntibus, Sl obicr vationi in uno aliquo fitu obfccundantibus. j Ncqp ctiam , quae vetcres in praecipuarum quarunda ci vitatum latitudinibus rimandis cx 1 proportionc Gnomonis (& umbrap prodiderun*" , ad amufiim ritc fc haberc crcdibilc cft, ' fiquidcm umbra? cxtremitas non fatis pra.'cif<: patcat , & longifiimu oportcat cfic Gno^ H ^ moncm. 1 i monc , cxa(fli(Timecp ad fuu planum di(pofitum, qualia in ipfo Mniuto pandat^Tacco ijl 1 ^L]uino£lialiamomcnta, circaqusehauc pragmatciani utplurimum €xcrcucrunt,iliis non tam prarcife cognita fucrint» atque ha?c poRulat operatio. Cum^ Sol c/rca ^^_qui ^ noiftia citinimc Dcclinationem varict , pronumcrat aliqualcm hac in partc committerc cicviationcm,licetfcnfibus oculorum noadcnodumobviam» Q^iarcca quaf de rehtto* nc Vmbrsc ad Gnomonem in urbc ROMAa PLlNlO referuntur , quod (it in zEquinoflns veluti $♦ ad r). ctfi ritc cxpcnfa,SoIis6|^ fcmidiamctro una confiderata pro^ bent quodammodo, cande nunc c(Te R O M ^ Axis Mundani inclinationc^quap olim fnit temporibus P L IN II, collationcmWrum faclacumns quar centumcirciter An^. nos a pra^ftantiflimo illo Mathematico lOHANNE REGIO Montano ifihic I cxplorata iegunrur» Attamen cum fcrupulus adhuc njovcr! queat i an fitis prat cifcijnt!* quitus comircfurationcs illaGnomomVaf acccptaf fint, nihilo fermcccrtiores fumus in hisquamantca. Nolo nuacinfinuarc,quod<&ipfa Ragiomontanidenotatiofluxafit, adeo ut fibi ipfi intra quatuor minuta non conftcs Quin& h2f c ipfa qua? attulit cx loco Solis nonfatis cOmpcrtoideoqi.Dcclinationcciusdubia paulo audentius protulit: Vt dc refraftfonc, atcp Parallaxi Solis, qua? duo ncglcxiflc videtur, nihil addam» Nulla igi^ tur alia rationc,quantu ego quidcm vidco.indubitatc expcriri licebit, an aliquatenus A x# is rcvolutionis Vnivcrfi,motuf6p diurnifcfe alterarit rcfpc£lu ccrti Hor/zontis in Terra prxtcrlabentibus aliquot fa? culis , quam fiuunc , ALEX ANDRIzE potiflimum (uti di^umcfl) Poiiclcvatioquamaccuratiflimcdcnotaretur,atopcumvcteriillaPtoIcmai- cacouferretur* Porro non folum hoc,e3:n^G Y P T O novitcrinflituta anrmad vcrfio commodi latgirctur,fcd<&multaEfixc Stcllapiflhic unacademcpopcra Ccxlitusdcnotarfpoflcnt, quar in noftris Horirontibus nunquam oriuntur ufq^ ad ipfum Ganopum^ 1 n Solc quo^ quc & Lunaaccafteris Planctis plurima ifthic tam in rcfradionibus,quam Ai)s ad eofim normam fubtilifllimc fcrutandam facicntia cxplorari : pcr qur vcterum ibi degcntiu an'* madverfiones limitari potcrint , at^ in ca quae in his Borcalibus \ocis dcprehcnfa fint fimuldifqui'ri:quatcnusvidelicctcumr]sconvcniantnccnc:multa6pprartcrea Afirono^j miaf in intcgrum rcfiitucndae" hinc provcnirc fubfidia : quae figillatim omnia cnumerare^ nimis longum forct. Vos igirur , llluflrifiRmi & Potcntifllimi V E N E T I , fi huc cximiam & laudc dip^* niflJmam curaadhibcrc, vclutiantca mihi devcftra prapclara intcntioncinnotuitnonde^ gravcmini, fcccritis fancrcm non faltc utilcm,diucp fruflra defideratam,fed(S: ad omnem Poflcritatcm inclyta? vcflraf laudis quaf alias latcclucct,memoria dignifllmam* Egovcro quantuminmccfl,huicNcgotioauxiliatriccsctiam ferrcmanus ^fivcln* mcnta^&mcdiaordinando,fiv^H«V.".'Btfil iiti 'iV'i;'iii 7iMiiainf'l7-i"-' \i"ii-- - ifihi 'g ' |lj^\__l. ' -^ • ' '■• - l" i •'■•'■■-'■''■■"'•-'-'-■- II ' iiiril •':'i'ti V 1 " •i il" DELINEATIONIS ^RCIS l^R ANIBRVGI, j QJ^O AD TtJTAM C AP ACI T A t E M EXPLlC A TI O, J ^SSiC^ R[£)ERICVSSEbVNDV S lau JatjTsi iiis mcinorLr,Rex Danir($<:Norv.igi'3r, &c. nulli I ^^415^'^ virtutc,tTiagnaniiTiitatcarc^inregrirateccdens,quianccannosdeccm ingcnti cum Ju^^lu noii faltc •y? Daniae&rubditorum fed 8>C adiaccntium Regionii fatis ccnfcrsiri annumageris.Ttatis quincjuagc- 'l^ fimum quarfunijdiuturniorc lane vica dignilsimus, modo DEO ira viram fuiiTet? [3 (inqua) op» ^^^ cimusRcx.cum praetcralias Hcroicasdotes crga liberlalia ftudia verclibcrali ^ propcfo eiTctani- mOjatq^intcllexilTet Aftronomiamintcr h^cprmcipem locUm obrinentCm , afummisrcmpcr Monarchis(S<: Rcgibus in fummoctiampretio habitam,multosc|? cxhislaudabihki-inca veriaros, nccminimamr.ominis pcrpctu Jtarc indc conl'ecafos,hanc in fuo ctiam Regno prjeclarc cxcoii atc}; fovcri duxit operxprctium. C^ya ' proptcr, ubimeilJ!usinftaurarioniopcramnavarc,arq?incapal3eitramultisiamannis indcadolclcentiavcr- farum pcrccpiiTer ; adeout huius continuandae d^adoptarum flnemperduccndjegratia,rcIic^aPafriainGcr# maniam ,qu6 quictius (SioportuniiTscidcm vacarcm,diiccdercanimum induxiiTcm, tncacccrfitum, utifthfc m D ania jdcm cxequcrcr,clcmenri benevolcntia adhorrarus cfi::(Si ipore oblara Infula celeberrimi freri Danici 1 Vcnuiia,com!.r!unit:cr(uiidiJiuai)f luennasppeJlata, commoditatem ir.iceCxieitibus rtud.ns il vi opcrj Jdiuli j Regio favorc Jargitus cft: veluti alias quoc^ huius nunquam fatis laudati Rcgis confilrj mcnrioncm 8>c mcmo* riam rccolerc foleo, cum non tantummodo dc mc,fcd &C tz tota re Aftrcnomica hac rationc fir exiitiie n^erirus, C^iare vnivciTamPofteriratem,adquam(utifpcro) huius rei vfusfruilusaliquando pervcniet,Serenilsimj ^ OprimiiiliusRcgisnomengraramcntecclebrarcdeccr, ExiUius iracf: prxftanril'simi Regisdecreco, arcj; volunrarcclemenrjjCumin diAalnlulaaedificiaAftronomiconegorioaptaioIide&manificeamcconfirucnda forcnt,el2gi locum maximc in ca aeditum^cum &C tota Infula per fealce extaret) prope cius quafi meditullium, ubi Arcem ex ipfo Ca:lo,cuius obfcrvarionibus infcrvjrc dcbcret,denominatam , dl Vraniburgum ob id di* Aamfundamenralifcrconftrucrcaggrcfrusfumjincipicnic^abAnnoiyy^^.fucccfsivistemporibuseandemab- fol vi;cutus Orthograpluam hfc fccundum totam eiufdem foriTiam $<. capucirarem.quantum ix\ plano ficri po ruif,rcpr3efcntatam vides. Parciculariavcro,qujein hacdclineationecxponendavcnjunt,inhuncmodumfc habent i quatenuj jifcri3,qu.Te peculiaribus locis annotatx funt, fingula indicarc datur: A Doinus praecipua in ipfo mcditullio totius capacitatis cxtruAa,(5(: pcr quatuor lua latcra xqualc quadratum efficicntia \n 4.Mundi plagas exadtifsime vergens,ita ut du.ie turriculaeMcridicm d)C Scptcntrioncm, ambae vcro val Vce Ortu (& Oc- » cafum cxquifife refpiciar.E.Porra C^ricn talis operc ruftico (& Tuicano copofira.D.Porra Occidenralis eodc ope ' rc elaborata.Habuerunt autc hac binae portae fupcrius duos Canes maiores Anglicanos cxcubitor es in con vcni* cntedomuncuia,utundi.padvcritantcslacratu indicarcnc. S, OiFicinaTypdgraph:ca,m2icr?s domus Idaeim parva forma quodammoiio rcfcrcns, C, Domuncula pro miniftris,ctiam niaiorem domum,quoad frontifpi- cia,&qujedam alia rcpracfcntas, F. Interior vallifatics. G. Extcrior cius forma cum fua difpofitionc. N. C^ua- tuor viae vcrfu^ ambas portaii(Siutranc^ domuncula ducentcs quae in^ . Mundi plagas ad amulTjm excurrunt, O. Quatuor ianux horcorii, M. Pcrgulae quatuor in illis fcmicircularibus vallis amcenitatis gratia difpofitJe, L. Hortihcrbarum& florum, H.Horci Arborum varrj gcncrisnumcro circitertrcccntarum,(&c. Atcj; hjec cft totiuscapacitatisdifcriptio. Habetautemvalliambitusfiguramquadraram,in mediofemicircuIariJnriima^naexiguisfvringamurmuncraUuuliriit Sic vaivmt 'variantque vices Terrefiria qntc^^ Sit tilnUus[oU qm C(xlum ty Sidera torfucSt OR. nmmmmmm-m m^^imm^m^t^mwmmm O RTHOGRA P HIA PR^CIPV^ DOMVS ARCtS VRANIBVRGI IN INSVIA PORTHMI DANICI VENVSIA Vulgo HVENNA, ASTRONOMIA INSTAVRANDiB GRATIA CIRCA ANNVM i;8o, aTYCHONfi BRA* HE EX^DlFlCATiE, ORTHOGRAPHIA PRAECIPVAE DOMVS ^^ mciS VRANIBVKGI IN IMSVLA PQRTHMI ^DANICI ^\ IIV.C.NKA \stronomiif inftauran- dajratta arca mnum i^So ^^ a IttHoj^E Braue ■»'■'■>• 1 ii m VV^ tSS,'- 1; Wfff-^i^B:^^ '•':Ms ICHNOGR^VHL^ £T £1^3 EXVLIC^TLO cidentaUs,o,Trafitus 4.>4d M~ 5 tn pojica in tre$ redxHi [unt, cdufium D. ampliaretur, atq^ in quoddm etfecretum Uhorato: AUnua OrientaluC.Oc. ^ulos re^os cocurrentes, ut Canaculuhybcrnufme hypo» eiut 4n<^ulopoll fornace paruu '^iumfp-i^ricum ejjetjn quo tn promptws ad tnanus iflhkoperi pertnmaius illud defcendendu Im rotans , qui aquas hinc inde tttr.D. Cccnacultbm illHd hyber- tibus L. GradMproajccnfuin Coquina^K., VuteuscomentUius hydraulica feruens er a^uas permurutran,cutes in finpilas inferiorei dillnbues P. Gradus quinci:, diflinctim erant furm, q. Pyronomico inferviebat^ne fem foret B.Fon J itquarium volubU cum lubuit,in fuhlime eiaculaba mm.E,Y. G.Camer£pro hofpi fuperiorem contignationem. H 40, ulnas profundas , artificio pcr fiphones hinc inde occulte Cameras tam fuperiores jMm pro dtfcenfu in laboratonuChy miam T Bibliotheca vv.Globusmdgnus Oychalcius nm.exhihitut V,Quatuor mcttf^proStudioJis,4.0imini tm tlatfo. ratono inferiori afcendentes, quam in quatuor anguis conclavium Y. Lecti tn iifdem concUvlbus. hittc mdedifpoJtlK C^era actus inf.^ctor propria mtentione facile difcernetM-elh^enda autem (unt hfc omnia in ea quantitate.rdutifundamento ma loris d •>nis (ut^ra depictje quadrarepoterunt: U< et hk coarctafionis loci ^ratU m duvlo quaji minortforma ext)tt>eantur. .1 HXPI. I C <• TIO Pi\RTIVM MiiO.ii' ET PKAbcJPVAE DOMV.^» S^'-i {?iCinaior5:pr.Tcipi!a Arcfs \^ranrD..igic.i?c!o)a.usan^e^xx'diiicari cjfpracltAnnoi ^^e". Po- lujcq; cius primii fundamentalcm lapjdciH, Vrer.iirinij &Poccntifsinii GaliiaruinR^ihiiiDana plufmii« Ann:sLcgatusAlaiinjficut>Dominr:sGAROLVS DAN2:./tVS,virinfcgrkate,vir tiite cS: rcriim ufu nu!li fecundu6,<&: Dov5i:rihi« infuper iibcralibus prjcclare imbutus; qui cum mc finglilari 6i co:->fUnfiamore,qu.uiii dai vixfr(obijtenirn anteOc^cnnjurr; setatisanrvoOctuagcfi- mo primo) prokcutus fuer;t_,mihi Si meis rebus plurirnum fcmper favebar.Et fimul ac domum hac con^truc •dam inreiiexir,fc primum iapidcm angularcmitthlc collocaturum iponte addixic. iMoxc^in Iraf|)kyrio quo dam laxo vcrba fcquentia cxicindj curavir. REGN^^NTE IN DANl^ FRIDERICO II. CAROI VS DANZAEVS AQVITANVS. R. G. L D. L, DOMVl HVfC, PHILOSOPHlAfi INPRIMlSQVfi ASTRORVM CONTEMPLATIONI REGIS DE- C R E T O A N O B 1 L i V I R O T Y C H O N B ERAHE DEKNVDSTRVP EXTRVCTifi VOTIVVM IIVNC LAPIDEM .uEMQrvI-^^ ET FELICIS AVSPICU ERGQ P. ANNO cl^ li. LXXVL Vi. ID. A VG VSTI. CiTna vcro dfcs is,fundationi dcfi:inatus,inftarcr,acccfsicoptim9 :llc DanaejcuSjComirarus ali^uos Nobilib, viris,cum quoci; quibukla do.^is ex amicis conibus.qui huic adui inrcrcircncjiii: dic Ov^tavo Auguli; mane cx oricnce Solc una cij f up.iuxta cor r2,Luna occiduu cardine in :2? occupancc,in omniu noitrum pr^iefencia lapidc cundcmlocavit,litandopriasfolemaitervinisclivcrfis,>.SrrucluraeOdogonales,inqu|b.i(iQagines cxcife4. Anni partesrcfercPtes,col'piciuntur.j6jS. Scptcm Caminiin unu dcfinentes vcrlusaiiftru, (Siah) feptc veriusJ3orcam,ifautomncsCaminitotius domus induob.locisdiftinCiim concurrant.N.Horologium^cuius capanay. iupcrius pender. A. Pegafus auratus,qui verfaf iJi indicc,i:ifra rabulatu iupren.ae Gamerjc oltcdit.vn- diCjVndc vcnti ipifct.lbir^ alius indcx in codc cento volubiic» horas mdiirat. Talt^ eft cxtenor facicsdcmus,fi veab Oriente fivc ab Occafu fpcCletur,(5<: fi Meridionalem partem quis cum Scptcn trionali conferar, candcm ct invenictformam,ifautomniafibiinvicccorrei'pondeant,i3<: c6pctcnr?Symmetriacoftcnt,proucin Archi- cedonicis,fiarfirjciolectdebitomodoconficicndalunt,rcquiritur,Quin & iubrcrranca^quaepundatislincolis | infcrius confpiciuntur,ficfunraccipienda:infraTurrimAuitralcquicquid cernifur,laboraforiuPyrononiicij,j quoad fieri potuit,exprimif;ubi i.Mcnfa eft rctunda in eius ipcditulho fita: in qua rcponantur ea,quar piwpaj! randaiunr.Numerusz.furnosvarrj gcncris circumcircadiipolicos utcuncs rcprx'icntaf,Eranrcj!nun.,)<).Tria balnea divcrfimoda Vnus digeftorius in cinerib.quatuor magni athanorei>,duo parvi , duo iurni dcliiJiarcri) in oercna vel cinerib.Vnus pro vefica magna,duplicib.canalib.adaptata, Alius iccret? iurnus cuin lairpadib. Duo revcrberatorr] furni,quorum unus m directum , alter per linca Hclicam tam apcrtc quam clauic rcvcr- bcrabat.Eratc^ maiorfornacum parselapidib.fcfaibilib.eNorvagiaallatiSjquasBcrgcnlcs vocanrzfiquidchj igncm fortiiMmum i'uftincat,&aifabrcelaporatiqueanc. Scd fingula quicin hcccrar laborarono.fi c>:poncda forcf,n5 o-^ucis abfotvrercntur. Qiijcinfra ipiam maicrc domum dtfigtiJta iunr,CeiJa'?, rc poi.toria,<5': p<:nu,in | dicans iubtcrranca,Vbi lanujc per quas hiic indc ficingrcfkus nu.j.Columnxautcm luftfntacuii locodilpoii- f:jenu.4.noranrur,SubBoreaii Turri luxta nu,j,Pureu)^iileCcmcnririus cernirur ^o.ulnasprofundui; cuius, poftCfi in Ichnographia ukcvior fir mcntio Numero ^.Ciil^c iunt Cemcnriciae,ia quibus cduha qujcdam conicr v;:H^pf® luisappendicibushincfnde extantibusprorlonpaucis Inf^rumcntisutut amplisjTthic commo- ^ E^%^ ^^ diipdhendis fufficcrent , tamen ctlm fuccefsiVe ccrtis dc caufsis plura adhuc confieri curarcm, ^J^^!^- ^"^^ ^^^ fatiscompetcnter iftis continercntur fpaciis, ut unicuihbet iuus ufus fine altenus obfta- c^w5^;iN@^ cuho conftarct> poltmodum circa Annum jf 84..in collc auodam cxtra Arccm vcrfus "dcridiem 70, circitcr palsibus minoribus i valio rcmoro Qbfervatorium quodclam fubterraneum Crypis divcrfis e fo* iido muro ab imo ad fummum cxtruAis confieri feci labore 6c fumptu non modico , partim ut in co quaedam ex proecipujs inftrumcntis ruco 6c firmicer difponercm, ne ab ullis ventis qu idpiam difturbarentur, arcj com- modius ufui infervircnr, partim ut Studiolos racoSj cum plures adcirent a fc inviccm diiiungcrem,& quibuf- • danin ipia Arce, quibuldam vcroin hifcc Cryptisobfervationcs cxequcndaspraemonftrarcm, ne fibiinvi- Icf m impcdimento ";orent, auc obfervara priufquam vellem , inter fc conferrent, AppelJavi autem hoc Ob/ lervatorum Danicalinguar^ l"iirra te5a confer\rab.-?ntur . quemadmo- j dumeciamad angulosBorrhapeliotea & Porolybicum quaedam aliafuo tcmporc dtiponercconftitucrarn. J Hjcc breviter dc ftru.^uris hiicc Crypticis di Aa fint, Quae fi omnia figillatim explanare vcllem, prolixa opus | foret deicriptlonc, Qjj ilia infuper Carmina hinc inde rjldem Cryptis aureis literis afsignavimu^ , idcm libcr | prim is Epiftolarumexhibccj utcadcm hic rcvocarenonfitoperjcprctium, t Arq; hrc de acdificiis Aftronomicis Cu indicaTeiatis. Liccc vero Iniulam cclebris Porrhmi Danic/, in qua I haecexcruximuSjhicapponerenon fiieritanimus,tamcn quiacTediti5Jieorfim conftirutiloci mentionem f^ci, J 5c quoniam iioec ipla [nlulaiam antca in quarto Tomo Theatri Vrbium a Clar.viro Dno. Georgioijrairn cx:. I prclla cftjlicct non fatis appofite incuria picftoris,idcirco cam hic paulo exacbius exhibendam duxi, 1 O j INSVLiE VENVSIA i.-.. '^ ,.■, . -■■— ■■ ■ . ^M^^,^ ■.■■■.■■ I lli^ vvLgo hvenna. DicriE» li I n i^TTTTyfmyrni EXPLICATIO HVIVSTO POGRAPHI^. . v ^Tt A- u.vituifur hx-c inluu in ceicberrnuo frero mclyti K egni Dani3e,quod Scaniart di^^Wft a Zelandia» >*. ^^y^.« . _ ^ /- ^i ._ /^ 11 i-o T . Ji*>. ;_ . u.>- l^f>.->s>i-> lilrvm iinirri ^^^^lquodcxav^levcrrusSeptentrioncert^crjamduobusdjitat^LandferooiavcriusEufamialtcmunico, ^■^Jii^^d qi,x duo in Scania fita lunr. Eftc^ Infula pcr le admodum alra, ac (i quis in montem aliqucni alccndc- rct.iupcrius tamcn tota plana,habefq[; in circuitu s.^o.pafTus maioresJ circa eius mediruihum.ubi Arccm Vram buUum ex3fdificavi,Policlcvatic;rive,quodidcm cft,l.uitudoab AiquaforeG.rr.^^.f4^- fummaaccurationc anobis ixptus citdepreheniaLongitudmcm eius anumprijiuis partiiim 5^.M.4.;.habito nimirtj rclpc^u airUrc- rice Mendianorum,quibus ufi funt Prolemseus 3c Copcrnicus ac huius qua ficri potuir,diligcntia: qucmadmodu inhacquadrataquocf figurarioneIniul>necGermanianonfinedtfFicultateconquircndaforet, ^ IN S VMPS l auteminhaecomnjaultratonnamauriQiJecunv|:cnimfiveebcncBcijsR«gff«,nVcprophi* rcditibusannuis coquircrc licuir,in eos ufus expendcbam;Vj de molcftiui & labcribus, ingcntiljiis , quos ift|iic' per annos «..fuftmui, nibil adda. Ex his dc alns qui vis cordatus facilc cftimafc pOterit,rtie ncn nifi graviisimu dc caufis prjeicrtim in hanc quinquagcnaria xtate, Sc magna familue copia Inlulam tanti conftantc,unaq? Patnam dulciiimam int^ caianguinc iun cios atc^ Amicos quampluninos dcierviiTc.Qux verO,quanracj? mc ad lioc Jm oulcrint volcns hjc iubticeo.lntcnm Scrcnifsimum Rcgcm meum Chriftianum IV.Dn.Clem.qui latidJttilMmK mcmorii Patri Friderico Regi horum ifthicfu.idatori Sc promotorinuperiuccci'sit,lubcti8 excuiatu habco.Nc- 1 queenim ambigo,fi tempcftivc&fulfjcicntcr,qu3e hocncgotium Rcgno fortal^sis non inhonorificum^oaccrnut, !iofiDropofitafulircnt,quinproeaquacftHeroicaNaturaR NQBIS ASTRQRVAl EXPANGBRH NORMA^. l SVPPLEMENTVM DE SVBDIVISIONE fiT DIOPTRIS INSTRVMENTOR VM, Iquidem fn ruperioribus , cum dc Inftrumcnt/s agerem , fubdiviRonem tranrverfalcm atc^ diop- rras non figuris exprefreram,qu6dca?tamcitoin promptu non elTent, Jubctidipluna, quoncgo» tium hoc rcctius intellagatur, hic fubiungerc. Divifionis itac^ punda habentis tranfverfalia rao- dus talis cft , ut hxc exprimir figura , in qua fingula dena minuta pcr lineolas in dccem intcrflitia equaliadifcriminatimpundisnotatafunt, fic<$ regula fiduciaequqdcunquehorum intcrobfcr- . vandum tranfiens ipfum niinutum gradus,quod quaercbatur promit,aut aliquo- ^tam eius partem, pro ut ab hoc vcl illo puncflo rcmovcri difccrnitur, Hanc autem Ltpfix in adolefcentia didici , redilineis quidcm Parellelogrammis, quibus ctiam proprieconvenit, accommodam ; Quam tamcnpoftea arcubusinlnftruracntis meis fatisappofiteapplicui, quemadmoduaj antc deccnniuminlibronoftrode Cometa Anni j jyr.circa calccm pagina 4^ i.his vcrbis innui:U'crf enim eiut iemon- 1 ^,T4tio rir^ilineis VayaUeltfgrAmm proprie conveniat . ttihdominm arcualibm etiam linen itt j tam exiU interftitiotquodiirei^a iinea infenfibUitermffett, ciira omne eitoris vcjligium con- venienterappbcatwr, Vt vcro hoc ctiam dcmonltratum hicaddam , eb fciolos forte quofdam, qui ea , quae non fatis capiunt, carpunt , fic habcvln afsignata figura A, fit ccntrum Inftrumcnti, eiu^cp fenjidiameicr A,0, afTumftur autem 0«f, parti^ cula in qua divifio ifia per lincas rranfverfas fit ea proporcione , qu3c cft i.ad 48^ qualis in meis Inftrument/s ur plurimum ufurpatur. Cumcj; A.l, ponatur par- tiuniioooQoboooo.intcgriCanonismaiorisRhcrici,critearundcQ,L2o83533:5j utpotc pars quadragefima owtava Radii, Arcus f,E, fic5o,/(S<: I,V,io./, horum finuszpoSfrr^.Y.l.Sinufcaurcmfccundus eorundem 42^oS,V,Y, quiadditus N.V,quod aequale eft O. f, facit N.Y.^og^^f (S^^i.In triangulo igitur N.Y,I,ad Y,rciiangulc,ndta funt duo latera N.Y.5<: Y,f ,quarc datur Bafis 1,^,210595208 unacum angulo N.J.Y.;i2.F,j./.!o.yy.4'7.///.Cuiaddicus Y.I.A.S^.P^fo.c Con- ficic N.I. A,)7i, P.i^./ 10. //,47,///. Bafis vero N. I. in ttiangulo rcdangulo N, Y,I,dividarur in dccem partcs sequales, ur conveniant uni rainutozjoj^tfjj. rc- praefcntarjc per I.B.moxc;^ in triangulo obliquangulo B.f, A, dantur duo latcra J,E.»o./A47.//ApriiH reperto : quare innotcicitangelus I.A,B,j,Ai.y/,7.;y/, qui tantummodo j. /. efTc debcrct,ita ut eo maior fit falrcm u//,7. ///. differenria faneinfcnfibilr, Similiterfi F.l.afrumaturnoveparticularueruntCcTigj^^-^ifg^, habebimuscj; rurius triarguJum F. I. A.in quo dantur duolarcra Fil,raod6 di~ duni, una cum Radio f. A. 6c angulo F,I, A, ab iifdem comprachenio , vclut an- tea ; exurgitq; angulus I.A.F,9./.i.//,(S",///,qui debcbat efTe 9'h exade, dcficicnte in ulrimo minuto F,N,t,//, ff.///, Pof ro ut circa medium idcm tcn tctur quod nunc apud extt-cmitatcs fccimus, inveniantureadcmrationcquaantcaprjmoangulusf. A. H. f./. 5. //.evott4S ajlra: ude /.STRONOMI iwW Cdgnomen, 'Ernejii ftUam genus Te lcriderice, longi gentis Glorid^ Teuchomciqi Sceptri i Suh hoc pdtrono Kegiomontiws fulfit \ohannes Vranit dccwsi Ciuem Parcajatalifq; livor llorte nimisproperata ademtum terrii removit ]Ue triangulos , lUe expolitam Mechjhicen dediti Quin Noribergafabricanieni Obliupuit, fiupuitq;C