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Dit boek hoort bij de Collectie Van Buchell

Huybert van Buchell (1513-1599)

Meer informatie over de collectie is beschikbaar op:

http://repertorium.librarv.uu.nl/node/2732

Wegens onderzoek aan deze collectie is bij deze boeken ook de volledige buitenkant gescand. De hierna volgende scans zijn in volgorde waarop ze getoond worden:

This book is part of the Van Buchell Collection

Huybert van Buchell (1513-1599)

More information on this collection is available at: http://repertorium.librarv.uu.nl/node/2732

Due to research concerning this collection the outside of these books has been scanned in full. The following scans are, in order of appearance:

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Mathematici et Astronomiçi

Quarto n«,

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SPHAERAE


ccekftium ratio,natura, 8lt;Smoa tus:ad totius mundi fabric cationi's cogni'tionê fundamenta»

XXXVI.


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I. VÄLDBRVS VBCTORJ S.

Si Vantumuideo me erga bon drum literdrumjludia ddiuuMt j dafußinere officij,tantum ldboro,ne quado ulla in me negU igentiit fufpicio cadere pofjit .Declardrunt id cum multacie \tera, turn in primis Plat o er Athenxus,fuperionbus diehut ____ 'per nos excitftMquibus erft forte plus profacultdtibuscon tendiffe ait}suideripoffum,minus tarnen ipfemthipro dehitofeci. Quod ft cui obfcuriora adhuc mea officiauidebuntur, expreffioraet fpero acillufriora brem reddentaairalisilla Ptolemaifutéeiui^ÿf m tandem commentatio ihe» nis.epuorum utrunfopus iamin manibus habemus : ut interea dtffimulem ^ praelare operam faam officina noßra.cum me magißro.tum Valentino eu rione, libris ijs nauarit, lt;juos infidé iam olim ipfarecepitdexicon illud Griedi dico,commentaria'ip LatinaP.Perotti,(S' A.Calepini,cum 'iheodoro er Vrba nogrammaticisufuibus utfemper adhuc qu'am fieri potefi commodiffimeflu diofis licuituti, it a deincepsfi non maiore, certe non minore turn fruüu atf commoditate quam antea hcebit. id quod prafertim de lexica Graco affir» mare non dubito, adquod excudendum nunc it a me confirmaui, ut eo édita facilefperem nihil amplius te,quantum ad hanc rationemattinet,deftderatu rum, Sed uale,ernunc quid in hoc opere tibi proponatur,cognofce.

Landauus defolidæfphæræ

lacobus Zicglcrus conftrudlione.

Proclus Diadochus Lyciusdefphærajfîueglo« bo cœlefl:i,{cholij s eiufdê Ziegleri explicatus» De canonicaper fphæram operarione, Heim'cycli'um Berofi.

Aratus Solenfis de fiderum nattiraamp;motu, fie inul in eundeincunicommentarfjs Theonis Alexandrini philolbphi.

PlanifphæriuniC,Ptolcmari,amp;^ lordanû

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lACOBVS ZIEGLERVS LA.Nj DAWS .BAVARVS, PAVLO BOM: BASIO BONONIBNSl S. D.

i Vom in Sapheam comentarer, poUicitus fum me eriam fcriptus rum in Sphæram Archimedis, i quam ego ei autori tribuo,quos 1 nia habeo perfuafum mihi, Ar« chimedem primum uel coftituiffe hanc, quam folidam dicimus,uel collocaffc in earn Relias fes cundum canonicas radices. Eius ergo conftru dionem datums pracfenti opera, fueram addis turus etiam ifagogas ccelitus apparentium re; rum circum terrenahabitationem.uemm quia ueteres cum alp, turn Produs, quomm ftudijs : conferre me no audeo,uerfati in eodem propos fito funt, ad ueteres earn ego partem remifi, des fumpfiep Proclü qui hanc abfoluat. Addidi tas mê locis opportunis fcholia, ad duxiep fenfa au toris ad defignatoru in fph gra circuloru exems plum manifeftum. Qua demu indicatione abs foluta,fubiunxi quafi coronidê paucis capitib. quemadmodum canonica ratio cocleftiü mos tuum reprgfentenir in propofita fphgra,in qua etiam ipfi operemureofdemeffeOtus concordi fymbolo,amp;^ quo eos operatur in codo poteftas nature. Hanclucubrationê tibi nucupaui Pau le Bombafi amico bene merêti. N eque ueritus fum, q? abiedcurus fores opeUamhanc, quauis a bres

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DB SPHABRAE SOLIDAI

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A Ptenirfphæra abfoluta ad femicircuK cir* cundudi caftigauonem, fuper diametro non minori palma 8ó femis, fiueutlibim cuicp fucrit,êó uifum oppormnu. Ea fphæra fi ex mc tallo eft,inargcntcmr. Sic enim profunda circu lorum Sf dcfîgnationû fient confpeÆora. Vel fi ex materia fiet, parentur très armillæ ex un a æ* quilatatione, quæ fint profun dæ in tenu s, à cir« cunferen ria digitos duos latos, per harum me« dias fuperfîcies ftribantur circuli uneq; earum ‘ nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;latere

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CONSTRVCTIONB, nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;j

latere,ex una gquilatatiôe per fingulas fuper no tis diamctralib.A c b o, amp;nbsp;A E B F, etCEDF.Inti mamateria a cêtro ad circunferentia inferiore, amp;nbsp;finientem profunditatem armillarum excins datur. Duæpoftea priores armillæ inferantur mordicus mutuo in communib. pundtis A B, His tertia inducatur fecundu fimilia figna prio rum C E D F, couenient^ tres fuper circulo mes dio profunditads,fic ut unam amp;nbsp;æqualem reds dantfuperficiem fupremam. Relinquunturfic quarts virj. uacuæ, quas oportebit folidamas teriaexpleri: uidelicetparantur eunei defubere, quoniâ hæc materia eft ari da, necinflaturudis auftris, nec dehifcit ficcis aquilonib.flantib.un deuicium globo fieret Cuneorumpars fit dis mata, fic ut interioricircunferentia pares fint in teriorib. armillarum, exteriori autem pares cirs culo medio ducfto. Pars altera cuneorum dime tur,ut interior circunferentia refpondeat eidem circulo medio, id eft, co nueniat ad ambitu exs teriorem priorij. Verumexteriori,fimilitcr exs teriori armillarum, fuperpofiti^ fibi reddantft mul profunditatem aflumpurum armillarum. His coftipenturuacuafpatia quartaru, interior conftipatio ordiatur ex utroqdateræ armillæ c EDF ubi ftatuantur latera, defcendatep utrinep c5tra A amp;nbsp;B angulos, copingant amp;nbsp;conf^ipent probè,amp; iniecto glutino côfirmcnt.Huiccôfti pationi altera,Slt; qux expleat globü inducatur, a i) uanG

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4 DS SPAABRAB

tranfucrfis cunei’s, ficutcoru frÔtesab armilla C E D F defcendat tota iUom proceritate. expies tis his quoque amp;nbsp;conftipads fpacrjs,compagis ncrurglutino fubimmixto. Hacratione cunei in diucrßi nitcntes,efficiuntglobû perpetuum, êC nulla uetuftate fatifccn tem. Hoc perfeCto, no ten tur punira ab utrinque fignata per fupremâ fpinam armillaru,per^feóionem ex omni late re mediam.ex bis pundis fcribatur duo circuli fuper diametris, quafi digitalib. poftea in ipfis pundis A B figatur axes craffi in(tar calami ari ftæ,aut eo eriam crafïïores,ct exeant à fuperficic fecundum angulos redos.Cuius rei examê eft: ftatuatur pes circini fuper media craflitudineas xium quafi centro, alter extendatur fuper circu lu iuxtà defcriptu. Is circinus circududus, ubi manferit undiquacp in circunferentia, axis eft correcTus.ergo confirmetur. In cos axes fulpen datur armilla, cuius diameter A b exeat per mes diamcraftitudinemaxiu. Interior autcircunfe rentia fitelimatafecundu æquilataoonemiphe ræ. Ea ergo armilla transferatur per integrum globum, iscp climeturfecundu illius canonem ad abfolutam fphærâ. Ei caftigato inducantur nerui tufi,ólt;S his glutinum,amp;cæra, leuigeturep rurfus fuperficics fphærâ? adcanonem, amp;nbsp;des mum inducatur candor ccruffæ, amp;apparata cft fphærâ.

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SVfpendatur rurfus canon in axes A B. con tadus diametri c kuiter fignetur füg fphæ ra. Extrahâturaxes,ôô locacôpleanturutcirci« nus figi in rjs poffit.Poli fignêturmaiufculis Ik teris,amp;colore infigni A B.PôftexpIoreturpun dumfadlumex C diametro canonis, ut fit; me« dium inter polos, amp;nbsp;ex alterutro polorû extens fo circino incurui crure in notam mediâ fphæs ræfcribatur infigni colore,qui diuidat circulus in partes quatuor æquas c e d F. Rurfus lu« per alterutro figno E uelF fcribat circulus infi« gnis ex priori æquilatatione,fuper fignis A C B D.Rurfus ex altero pundo c uel d fcribatur cir culus infîgnis ex eadem æquilatatione fuper fi« gnis A E B F, Circulus A c B D fuper quartis di« uidat in quater xc. partes. Infcriprio fit ex E ÔC F per notas denarias uerfus A B polos. Item fus mantur arcus quatuor in diftâtrj s tropicis gra« duum xx111. amp;femis ferè F G, E H, a F, amp;nbsp;B K, Fixoep circino in L uel K fcribat ex priori æqui« a gt;nbsp;lautionc

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latationccirculas infignis c G D H. Poft hæc duo circuit CEDF,amp;CGDH diludâtur fccuns dum quadrantes in quater xc. partes. Porro in circulo c G D H fîgnenturtrigefîmæfecîHones, ordientesexquatuormemorads fignis,pcrhæc fegmenta xrj. amp;nbsp;notas L K fcribanturcirculi ex priori æquilatationeomnes infignes, hi parrien tur zodiacum,amp; fimul totarn fphærâin partes ^quas xq.Scribat apud c Aries,fiuehuius nota 'Y'. fequêti fpado uerfus G Taurus V- Hineges minilE.ExtraG Câcerçô.poftLeod%. poft ^. ultra D Libra ,£3. H inc Scorpius m.. HincSa^ gittarius ^. ultra H Capricornus yo.p6ft Aqua dus **t}.poftremopifces )£. Diuifionespduos circulos numéro denario fignetur, S^ quidc in circulo c E D F,cx c perE d Feounuanumeri fucceffioneuR^ in ccclx, Vltimoex polis a b feribantur

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CONSTRVCTlONE, nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;?

fer ibantur atrameto quatuor circuli per media figna H G amp;nbsp;L K. Ite cxalterofigno g uelH,fu matur latitude zodiaci utrin^ gradus vi. 00 K polo: extenfioneautem perfîngulos vi.gradus borealiores ecliptica ducatur circuli atrameto» Item L centro,extenfioneaût perfîngulosgras dus vi.au(trailores durant finguli circuli. Hæc eft défignatio fphan*æ.E rgo reponan tur axes in priores fedes a b, amp;nbsp;corrigantur fecudumde« feriptosex L Slt; K circulos,firmêtur^ neep poft bac ufquam moueantur,fintautemproceri mi# nus medio articulo digiti.

DE ARMILLlS CLlMATVH.

P Aren tur armiUæ tres ex métallo. Latitudo fitutfuperêtquaquauerfum ambitu fphæi ræ tribus lans digitistuidelicet pro mêfura fphg rsc,quâta aflumpta per nos eft. T num laminas rum una fit quadrata. Duæ fuperent tertia pars tclatitudinê.In ea qup paribus lateribus,aflum pto umbilico fuper eo educantur diametri m b s amp;nbsp;R E c,defcribaturcp circulus fuper E figno, extefio R paulo mêfura fphaerg : nempe quan tu occuper granum canabi interieÂu,ôC fit inferis ptioexM E R contra R amp;C ingradibusxc. fus per etiam extremo margine fiat fpatium circulo rum. ld diuidaturin partes æquas xfj. amp;nbsp;fuper tineis eduólis ex centro fcribantur uentoru nos mina» fuper M aufter, fuper R eunis, fuper s fes ptentrio,

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f D B s P H ÄE R AS

ptentn’o, fuper C fauonius, amp;nbsp;rcliquorum no^ minaordine{ùo,ficuthæc nemo no nouiuRes lique laminae quadrent diametris. Sed dug qug tranfuerfacfunt longitudini, diftetafronribus per menfuram femidiametri E m tabula: prios ris. Vna ergo quadretur, amp;nbsp;quidem tranfuerfa fitM E s, quacautemperlongitudinê,v E D.Ab tera quoq; lamina quadrilaria diuidatur,amp; dia meter dus tranfuerfa R E C, quæpcrlongû v E D. fup R D C v fcribatdrculus ex prima alEims pta gq uilataöone uicina fîahæræ, atq; femfeireu lus R v C diuidatur fuper utroqjmargne,intes riori amp;nbsp;exteriori in partes utrinlt;^ xc. Fiat^ ins fcriptio exterioris marginis ex R 06 C contrav. amp;inferioris ex v contra R 8ó e. Superautêm d S v lamina fcribatur ex interiori priorum gqui latationecirculus A F B ae. diuidat^in partes quaterxc. amp;fiatinfcriptioex AEcontra A amp;^ B. Âb hoc extendat circinus ad fpatiu prope lati digiti,8^ fcribat drculus alius diftas a proximo non amplius grano finapis intcrieélods quoc^ diuidatur in partes bis xc. 06 fiat inferiptio ex s contra v,item ex v contra m. FaCtis dimenfio nibus circuncidantur extrema tabularu ad abs fôlutamrotunditatêfècundûfîgnaR s c M,amp; R v c,amp;SM V s. Interioraquoquefuper intima circuloru defignationedtemarmilla A F bae to ta liberetur ab armilla fua ipfius fuperiori fuper fpatio interieedi milq, ficut pumfia fuperioris

non

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GONSTRVCTl Oquot; N’S.

ponuiolentur.Poftidcomponanturoniniain corpus unum.Sphgrafuis axib.A B fufpêdatur in armiUam afb ae in fîmilia figna, fît^in ope re probato diameter apud a e fignum jrefte infî ftens fuper medio circulo c E d F fphæræ.Sup« ficies autem armiUæ, quy præfert defignatioes, ibit per mediû axem A B fpbæræ. Poft h sec apte tur axis ipfi meridiano in v puncto uerticis gt;nbsp;ex

quo tanquam cardine polari moueant quar tæuerricalium v R, 8^ v c. uiddicet accipiat duplex craffitudoari millg meridiani.Secûs dumbuius menfuram ducatur in planicie diai:

meter A B.Sitquocppropofitalamina,ex qua as xis perficietur. In ea ducatur linea c D conrinês diametrum a b ter cum vrj. 8C ex C D ducantur perpendiculares C E 2lt; D F. Ïungantur quoque E F redà. Eius quadrâguli duo latera C E amp;nbsp;D F fintlonga, utpartes virj. qualium eft v totalatis tudo,fiue profunditas meridiani. Harum affus mantur duæ 8^ femis ex C D 8c iungantur redà G H. Eius quadrâguli CHEF duo latera diuidaii tur in partes iiii.æquaSjamp;punélaiungâturres lt;ftis. Sic delineatalamina,complicetlateribus C G Eamp;D H F,8ôcaftigeturadteretemfigurâ,red detcçmodulumaffumptu a b . elimetur fecuns dum oppofitas ex diametro partes pridê affum

b pt3S

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OB SPHÄHRAB

ptasperquams abimopedeEF adfinemc H^ fic utfilTuraarccècompIccfatur craflitudmême riJianijpforuin^bradiionim ge hf rotun« diras complanabitLirmallcoIo ad æqualêfupcrc ficiemfui Ô^meridiani, fieep axis A G ß H extus berabitdecenter ultra utrinq^ fuperficiem incris diani, prgftabuntep iequeno operi commodita tem. Inde parentur axes duo, quibus duæquar tæ v R amp;nbsp;v c fufpendan turin priorem axem, in eo^uoluatur. Accipiaturcumcircino fumma craiïitudo fuper diametro axis prioris,fecundiï eius menfuram ducatur in planiciedimetiens A B.Sitquot^propofitalamina exquaaxisperfie ciatur, in ea ducaturlihea C d trib.parub. amp;nbsp;vqe longioripfa A B, ducanturex C D perpendicula res c Eamp;D F. Hæc latera fintlongaad menlura priorum A c b h. iunganturreda E F.Eius qua drangulilaterac d óen F diuidantmpartes üp, æquas, amp;nbsp;iungatur lineis parallel is: media fit a H, quæexeat m k , fit^ h k quanta G H. Eius h k accipiaturmediû fignu L,unde exeat perpendi« eularis m n par profunditati quartæucrticali,iîc ueea deniep paulo contradiord pfi quotp h l K ducantur utrinep æquidiftâtes pro craflîtudinc quartæ. Extra has æquidiftâtes,amp;: lineam men quiequid lamin æ eftrefeindatur. Quadrangue lumquocp c E D F fuperlinea E F, liberetab E F M N ab extremis finibus ufcp adaequidiftantes, utrinqueipfi H L,K,tanta parte foluni coh^reant , duo

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CON S t R V C T t Ö N S. * duo quadrangula. Poftea c E d F leuabitur, fic ut G H ftet fuper piano

autem c e d F in figu« ram terete, inftar axis prioris, coibuntep late ra c E 80 D F lineam us nam, reddetep ea figu« ra teres interiori fua cir cunfereria modulum circuli deferipti, fuper A B fic caftigatu, utas xisindutflus priori cir cum eu uoluatur cons tigue,nee^ardHus, ne« quelaxius. Latera des inde M b amp;nbsp;N b fuplü neisaequidiftâtib. ipß H LKinclinabüturdes orfumadangulos ins teriores reeftos fuper p quidiftantib.denicpfi nes MN diftetmutuo

fecun dum paralielas. Eoaxe brefafto, paretur aUu s eo dé fch e

mate propofito, qui huic in du«

ftus,circum cum uoluatur cöri mie.In hac iftud tantumutabitjdiuilalaminain partes quatuor, i b * dueämr


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«« nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;• ©B ÔP AAE RAS

ducanmripfîs C e utrinc^ æquidiftâtes 0 P, amp;nbsp;QR paulum disantes àmargimb. PoRca lamie na rcdudla fn axem,is dimetur toto corporcme dio inter latera o P amp;nbsp;q,r Jn reliquis paretur fie J eut prior. Quoniauerohiaxes in an* gulfs H infiftutinfirmfus,qjutquartis v R amp;nbsp;y C ferendis fufîîciant,fuerit ne« cefle addere his à tergo cathetos,ut K h C.Ergo axis pofteriorindueaturpriori. Siemu tuo inducHsjaddâtur ipfis à tergo catheti, quo« rû latera G h fîntpaulobreuiora ipfis axib.præe fertim in axe priore fecundum fpatium o P po» fierioris. Fit hoc opéré, ut duo axes fibi ppemo cohæreant.fic rite coherêtib.omnes fimul com«

miiTuræconfirmêturillo glue uno metaUico fuforio. Demû ipfis braches M H N inferâtur quartæ duæ V R amp;nbsp;V C in moe dum hune. Axes G h ftatuans tur medrj fuper diametrum V d in media m lie neain v uerticis, amp;nbsp;communem duabus quare tis V R 8c v c. Lateraautem L m 8c L N defeen

dant utrinqueper latera quartarum, eas^ ardte comprehendant. Diriganturautem finibus m 8d N redlè in centrum circuli, fic^ correda cone figanturutrincß binisdauiculis, ne quartæ di« naoueriabbabitudine centri poffint, Spatium quoc^ quartarum, quod eft à diametro ad bras diiajuninq^refdiidatur. Intra hanceniminae c * nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nitateiTL

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CONSTRVCTIONB.


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nitatem fufeipietur crafTitudo armiUac meridias næ, Ambæpoftea quartæ refecabuntur fuper media diametro REC dereliquamedietate R D C. Reftat difpofioo indicis. In aflumpta lamis naducaturlincaG Klongautin operefuperio« ri,exearcfecetur K H. Eiducanturæquidiftan« tes quæfatisfaciant crafficiei armiUarum, Por« rbex H ducaturpcrpcndicularis,atq;huic alia G k nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;equidiftas ex L.Piniscç um«

s H U

ufquetcrminctur fuper m amp;nbsp;N. Porro ex æquidiftâtibus apud H ducantur duælineg, quæconcurrantin G.Quicc quidlaminæ prgtcrcacftcx= tra defcriptioncm hanc refes cetur. Tûc H L K(quod fieri

etiam in fuperioribus oportebit)reuocabitur à recta fuperficie ad portioncm circuli fecundum conformationem circunferenoæ unius armiU larum.Conus autem G in H bafi erigetur adans guluniredlum fuper K H, ut apex G rcfpondcat inlineam diametrieduélâ ex centre per fedtiof nem qualemcuncç armillarû, utq; angulus mas ncatcorrcAusaddeturilli quoque cathetus k h c.Brachiaautem h l m,amp; h l N demittêturin« ftarpriorumadangulos red:os,rediscp finibus fuis fpcétantibus in centrum:fic utcomprehen dant latera non quidê aréle ut in prioribus, fed ncq^laxe: uerum indent contigue, ÔC moueri b J Doffînt

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B » s F M AB R AB

portint per crepidinê quarte, cui index pro tem poreamp;obferuatioiieinfidebit. Hanc fâbricam axiculorum amp;nbsp;indicis fuin prolixius amp;nbsp;diligen dus executus, quoniainnoaliudeft ingenium, quohæ quarts præcipue aptari portint fccuns dumcanonicâorganorû operations, amp;nbsp;fuerat meo ludicio difFicilior,q ut artifex camexfemet conciperet. Etficdeniq^difficilisubi leuitenn^ choatarelinqucretur. Âdmultaautê organ a ÔC caprgftantiflimatutpote adfph^râ hancfolidâ fupficiei cœleftis: ad altéra fupfîciei terrât ad ar« mi lias, fi libet Ptolcmpi meteorofcopiù,organû Iphæræmundanæ,ad organa^ fingularu fphe rarum planetarum,tam eft necertariapars hæc, utpræterhanc iftaperfici nequeat. Sed tandem port longam quafi digrertîonem, ad coformas tionemorganiredeamus.InarmillgM RS C mes dictate M R s,ducaturæquidiftansipfi m s fecun dumcrartitudinêarmillæaltcriusM vs D.Pbrt exinterioricircunferentiautrinq; apud M amp;nbsp;S uerfus exteriorem (umatur diftanria quanta eft latimdo armillæ a F b, a e : hæ partes climens tur.Poft accipiatur medium refiduc armillæ ins tegre uerfus exteriorem circunferentiamutrins que, amp;nbsp;medietatesexteriorcs elimentur. Super autem diametro R C,diuidaturtota latitudom panes très æquas,amp;medig pertundanturfuper media diametro R c. In armillæ m d s v medics tateM Ds,dueaturæquidiftâsipfiM s,fecundu craflitus

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CONSTRVCTIoNB.

craffitudinemcius m R sc.EtdusIaotudomc«s diadiuidatur, amp;nbsp;medietas elimetur adrcunfes rcntiaintenorititrincpapud m amp;nbsp;s.Super altee ra diametro quæ apud D defcenditin pedê me: diadiuidatut fuperT,amp;medietas à bafi adT eÜ met procraflidearmillsc R D c, fug media linca


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•P^ / DE S P H AB R Afi. gt;

D T, Sed SCrdfqua dus medietas fin dat, ut Hac parte diduci diuadcariç poffit In terriæarmiU læmedictateRD cducaturgquidiftansipfia C pro crafficiearmillg m R s c.att^huius lautudo diuidatur in partes tres æquas', Só extremæ duæ refdndantur, extante media utrine^ fuper altes ra diametro quacapud D ddcenditin pedê, acd pi'atur ex pede diftanua T par priori.Eius armd iæ quod fupra T eft ebmetur fuper media diame tro T D procraffitudinearmillæiîmiliufignos rum. His omnibus incifionibus coaptaus, ars milla A F B AE, fimulcumfphxra confixaims ponamrin incifuras apud M 06 s armillæ MRS C.Sic utambarum interiores circumferenriæus nam facian t æquilatati onem ad globu m, obfcr uetur ne mutetur facies. Verum quæ defignata eftarmillæ AFB AE,refpiciat R fignum alterius. Poft, armilla M d s V inferaturin illam m R s C fecundum fimiliafigna m Sós, Ô^eoueniant fis bi fecundum cxteriorem fupcrficicm.fi quid in altera intortû eft corrigat, ftabitrurfus armilla A F B AE infuperficicM VSDjUndeexcifafuit. Fiftura reliqua bafis ab intima circuferenria ad T cofirmetur rurfus,per induclam tranfuerfàm laminamlongamlatamqj minus digito amp;con fixam.ArmilI^ autem dimidiatæ RDC bafis ins feratur alteri bafi, fic ut duæ ftent in una fupers ficie. Interioruero dus ambitus coueniat cum prioribus m R s C, amp;nbsp;A F b ae in æquilatatione

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CONSTRVCTIONB, nbsp;nbsp;nbsp;nbsp;nbsp;n

adfphgram. Capitib.aûtR amp;nbsp;C inferaturin per« tufas partes alterius in parib. fignis. His rite ins fertis, S^ fefe uiciffirn mordicus complexentib. axis A B G H imponatur armillc w v s in v figno, fic cp finefuo E F tendat rede in centrum,amp; con figatur. Fron tes quoep quartarum v R amp;nbsp;v c as pud v circûcidantur in rotundum, deindefuis axibus fufpendanturadaxem nuncconfixum, undetanquamex polo defeendâtfuper fuperfis ciem MRsc,experiaturcputfineuicio quaquas uerfum moueantur. Quodutcaum fuerit, im# mittatur ftridim amp;coadèin cauum axis primi cu lato amp;nbsp;plano capite, utcontegat amp;nbsp;contineat axes quartarum.Poft hæc diuidatur quartsears millarum MVsamp;RVamp;c v,fuper fumma atCß media fpina in partes quæquepro fe xc. affines his quæ per card fuperficiêantea digeftæ funt. Canonium quoqi fiat, quod dirigatlineam me ridianam,uidelicetin fuperficie armiUac m r pro xime M,fiat cauum rotun dum inftar fciotherici compaffi: perbuius tympani centrum ducatur parallclaipfi M E s, ÖC in centro figatur aculeus, cuifuperincumbatlingulamagnetis nutans ad omnempofitionem,8óos tympani claudatur cryftallo.SedS^per fuperficiembafisfubtus M defcêdat pcrpendiculum parallelum diametro V E D,fecundumrationemline2e X Y. Hoc pers pendiculum corriger fitum organiad planiciê horizotis. Hæc eft tonus confirudionis ratio, c Proderit

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It nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;DSSPHäERAS

P rodent au teproponcrccfiigitni opens in den facharta,amp; in cacxperm totaconcinnationem extraiacfhiram.Nequeenim omnis comnaodis tasfatisdefcribi, ncqucoinnis error fem cl fans caueri poteft,

1 N D V c T i o.

PRimi qui ccelitus res ad diiciplinam addu« xerunt,non potueruntinuen ta fua explica refatis, nifi organum coftruxiiTentexemplum cœleftis corporis,quod referret circulos cognacs tos, amp;rcpracfentarctortus,occafus fiderum,actf ccdioncs ad climata, amp;nbsp;recefliones, deniq; oms nes cuentus, quales plurimi ex cocli conuerfios necontinguntcircum ambitum terrenum. Br# go propofucrunt effictum organum: quod du plicieffigiepofteritati commendarunt, unain armillis corporalib. quam uocarunt pertufam, * altera in côrinuafuperficicabfolutæpilæ. Etha betutraquediipofino eandem poteftatem, Sed placuitProcIofphæracôtinua, qualanpridcm coftruximus, amp;nbsp;qua ufos fuifle ucteres probos autores fatis cóftat. Ob perpetuana enim fuam faciena, amp;S lineares ten uiffimos circulorum du# dlus, Óócceleftiüimaginum comprehéfionem, multócognatius cuidentiusep fubindicatcode# ft is corporis habitudinem. Prior autein forma armillarisutneceffiarqs quidem ncgocio circu# lis con dat, fic r cliqua ipfius, quia inania fun t,au ferunt

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CONSTRVCTIONB. nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;T»

feruntocuUs cum crafficie materig, turn ipfa ina nitatcfuperiorum phantafiam. Fitcp dum circu los fphærales tantn uidemus, requiramus fubs inde corpus qualecircunfcribut. Sed habet hec eriam immenfam utiUtatemaliam, quanta fphg rafolida præftarenÔ poteft:dequaalio loco rur fus dicemus. adeo alteraalteram præftat, amp;nbsp;neu tra alteri ufu concedit. Vtra tarnen utainur,con uenit concipere animo rationem, qua propoG« tumorganu fub faciem cocli coponatur. Qtio enim modo umbra 'a luccfua nÓ recedit, fed hu icillafecundumlinea refpondet: eo modo fphg racondr ucta non recedit ab ætherea fph grazed huius circuit circulis illius,^ panes panibus,ôi totatoti fuperincumbit. Ergo fi quapoteftas fit Héla nobis, fiue quia ea fada nó fuit,referamus faltem imaginatione centrum fphæræ in pofitis onem centri terræ,fic qubd duo hec centra unu illicelTeintelligatur, quomodo duæ gemmulæ rorisin unam confluant. Hac imagination efu perflciesfphæræ noftræ ambibit centrum unis uerfi,non fecus atqj fuperficies fumma terræ, ÔC cœlum illud ambiunt. Deniejj ftatuaturillicor ganû, fie ut ipfius linea M S exten datur in ter aus ftrum etboream ad canonem magnetis.Supers heiesautem armillæ m R s c in planicicm horis Contis mundanifecundu direcrionem perpens diculix Y. Hocfituoraani inteUecto circu cens trum mundi, quæcunque punéla, amp;nbsp;quicui ; qj dreuli

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drcunexcœleftî fuperficiein centru pcrueniut, quoniam peruenire nifi fahre faÆr fphæræ mteruentu non poflimt. Sequiturutfadâtin cadefignariones fjfdem nomi nib.amp;rrationib.quibus m coc lo cenfentur.Odo enim ambo buscodo amp;nbsp;fphcnr commué ne centrum £,amp; porno cardia nis inter id amp;nbsp;mendie peran^ gens E M, porno cedeftis am^ bitusM N.Sphacracautemno#

flræ A B, (ïgneturincodo quodlibetpundum, ut c, un deperueniatredain centrum. Secat li* neain A b, fphera d pundum fimilis ranonis ei in cedo.utq; arcus M c, ita arcus A Djquiauterq^ uni angulo E fubtenditur, ita punda pudis, amp;nbsp;circunferentiacircunferennæ, amp;nbsp;totafphæra to ti cœlo refpondet. Sed putabitquifpiam obfta* re huic aiTumprionfquia ftatuerefphærâin cen tro uniuerfi non poflumus, propterea^ relatif urdefignariones afemutuó diflidcbunt,quan tuin diftantcentraamborum fphgræamp;uniuer fi. R.efp5demus,hocnópoflèinfirmareafliim prioné.Habentquidan terræiumma diftanna mcmorabilêa cen tro. Sed ubi terra tota adcodi ipana coferimus, id quod noftro fieri negocio oportet, rota quarta à cen tro aflurgit,uicem nifi pudi tenet, qu manifcRis experimêtis alio loco often*

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oftendetjamp;f nucutreceptu uoltJmus.Ergo redi mus ad affumptionê noftrâ,ficp deinceps trada mus fplicrâ hancin terrg fuperficiepro cœlcftis etfuperficid experimêto captan do,omnes lincg circuli i ntcllcdti egredi ex cêtro organi per quaG cuncpipfiusfeâ:iones,perueniûtreâainfupers ficiecœleftiineiufdemnotæ circulos amp;nbsp;fcCtio= nés. Poftea,G quæProclus cœleftium fegmens torum definierit,nos in fphæraexemplari •' defignabimusjidquamuis inaltero fiat, tarnen in utroc^defigna?

tumaccipidebdjit. '’

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PROCLI DIADOCHI SPHAERA, THOMA LINACRO BRITAN

NO INTERPRETE, Ddtxi o-folit.

Xi's mundi uocatur dimetiens ipfius, ^xis extrana,poli niudi feu uertices funt nominari. H o^ rum alter feptêtrionalis, alter auftrinusdicitur, Septen trionalis, qui femper in no dra habitatio neapparet.Auftrinus contra, qui femper, ut ad noftrumhorizonta,conditur.Suntautêin terf raloca quædâ,in quibus polus,qui femper no# bis cofpicuus eft,iis qui ibi degunt haudqua^ cernit. Qui ucro nobis perpetuooccultus eft, rjfdemcófpicuuseuadit. Rurfus quoeplocum quêpiâ in tern's inuenias,ubi ambo poll æqua# bilemin horizuntefitum haben t.

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In noflm,) iioflra habitatio eßab Atthtopum climate fertmens m bore» tm, atfiseß primus [nusfphieran tribus quot Proclus explicat. iM autem Teprit[entatur,AE fignumfubaquinoâtalemoucturexuerticeV uerfus M, frcundumlt;juam bbuerit diflantiam. Hoc fitu B palus continue leuatur fut fra horisgmtem ce huiusfignum S, undefemper apparet. Sunt tamen.y h efl alter fitus fphiera, quern habent loca ultra clima Aethiopum uerfus au firum.qualia repererunthac atateHifpani. Ïta autem defignatur, AE fignu moueturex Vuerticeuerfus shorisiontis perquamlibueritdtftantiam.lioc fitu B polw defeenditfub horisiontem apudfgnum S. A uero auftralis con» fpicuusfet, leuatusfupra horizontem apud M fignum. Rurfus.) h eß ter tiut fitus fphttra, quem habent inca media A ethiopum,funtif fub perpendi culoaquinoflialis, Uaautemdefignatur,AH figiumreponiturfub V uertu eem.üoefitu midi,palus utertp A cz â,confpicitur in plana borizontit apud S cz MAsfitusfphtera ifiâtur réélus,priores obliqui, Hacforfan manifeßio» ra cuipiam uidentur, quim ut extra autorem debuerint fingulariter enarra» fused cÓuenit,utficut Proclus exhis init^s, qua nulli ignorata funt, alia du titgrauiora,ficnosadfequentiumfphteralium rerumoßenfione,ab hoc art dine legitime ueniremus,

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’esttgii^v/biy é M^ios Siu^àmiy ctJiC uJÄ Sin^x uî^H Tjotin^ TOt T- K0ir(iÿ^t/ltà XbKhHTXtfoTrtKOS^ hrHljUftVOS 3 KVKÄOS if^y 5 (ikyisos -r ifftv^i Tirx^xTiiHAuii KvxÄUif^ o t/U}(0T«itV' tintos VïTO Ttf C^t^WOS^ USi. H(UKVXÄIOI/ fiSj^ •^k^y«y istt-f[.x(i€xi'iStu,H(jiiKVKKtoi/ Jê ’V^in) ’np ó^i^ovTx^itp’ » yivé/a^ vos 0 HÄtOS quot;^S ia-ÿia^lxs TirOtamp;TOUyrWT ix^tVHp amp;nbsp;liv ^dt' V07rU^iv[u/^ xiia^ivès lt;^ ipOTTiKOS KVKÄ0S ^lgt; e V0TM7X' TOS TÓö(/ quot;Gab -r uhiv y^x^oi/Jbiait KVKAtoifiKXTX tIw voi -r Koo'A«» yivoiMiVHp ’T^is^o^Hp^i^' » y^^ofj^MOs rUf ^ei(ii^tvHit •jpoTTU^ mt^TXi.r^ » » {nytsH (iXè 'srxa-wy np ^ tS ^vixv' Tw vvfiTriri^iêT^ii^xytsH Jè »(ikfXtinr« (Jkv rot Tiu/yet(ii ^tvllb -^OTtLu^ 0Vgt;li7t TT^S liilt;rH{i^^tX() TffX^0lt;/lli\jK() 0 HÄtOS ^iOO^^TOU^xX^' Ùâi dx7t^K (ii^» 7J3i7mxa 77$1 KOa/ilTy/tO Ki' Kh^rta »9 äTOs'^OTTlKOS. AVTX^KflKOS J^k àh KVKAOS KTOS K^ ^XfAHAOS tS K^KltKMt ty ttfxojfó/nvos ^ Ó^t^V^S Kxf tp (TH (M0(/^amp;ohos vssrèyupxTfoAxii^xvi/iivóst^uToeKet/at/x •? xs^oiii (^ Tffewns »t^P ’^P KÓ^ctfx^ TSiy 5 “O^gösgyMtwi* l. KVKÄ(6(l,(iiyiS0S /\ ^y 5 tlt;rH(ii^lviSt i^»s e^ Of TfOTTlMh iAoèytSOl JèyUS 7I^S quot;^ Hlii7i^Xll OiKHTiy^Ot X^KflKoL 7X7X5 t/è 7XS KVKÄXS J'^ v^^P X7rAx7as, AÓytü 3ia)^97xs tx t^ tSp «s^uy SitnoiSy y '^ mtths c/ltó^if^xs Sao^ixsyty H/ii7i^xs i7rt votxs J^iX7V7rxiAvovs* (iévosyXjx^ 1^ Kotrinü kvkäos ^p M^H-ns o 719 yKAxK70s»0( Jè ^t7roi Aoyefgt; aai Sito^HiK»^

DE CIRCVLIS SPHAERAE.

/^ Ircuïorum fphæræalfj paralich' funt, Guc V_7 equidiftates,alq obKqui,alrj perpolos du di. Acquidiftantes funt,quibus qdê cum mun do poli funt, Suntautê hi numero quinq? ; So ptentrionalis,SolftitialiSjAequator,Brumalis, Antaróncus. Septen trionalis igitur circulus eft is, qui omnium,quos perpetuo cernimus plane maximus eft, qui^ horizontêfolopundo contingit,

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contingit, totusfupratcrraminterceptus. Inter huncquæcunqueclaudunturaftra, nec ortum necoccafum norunt, fedcircapolumuerti to* ta node cernuntur. Porro is circulus in noftro tradu,àpriorimaiorisurfæ pede deferibit. SoP ftitialis autan circulus is eft, qui omnium qui à foie deferibuntur maxime feptentrionalis habe tur. In quem cum fc fol receperit, æftiuam recia procationem peragit, longiffimuscp totius ans ni dies, breuiffîmaep nox cric Poft autê recipro cationemnequaquâ ultrauerfüs feptentriones folem progredi, qui potius ad diuerfa mundi re g edi cernas : unde 00 tropico græcè nomen, quator circulus eft is 5 qui maximus æquidi« ftantium circulorumftatuitur, ita nimirumab horizontediftedus,uteius femicirculus fupra terrain, alter fub terra condatur. In hoc fol dua plex acquinodium, uernum,autumnale^ facit. Brumalis circulus is eft, qui omnium circulorS qui afolecircumadunudi deferibuntur, maxis me ad auftrum pertinettin quo fol brumalem re ciprocationcmfacit,maximacp totius anni nox, minimusep dies efficitur. Pofthanc metamnes quaqua ultra progredit fol, fed ad altéras muns di partes reuertitur:undetropicus hie quoque quafi uerfilis appdlat. Antardicus uerb circu lus, æqualis 2lt; æquidiftans feptentrionali circu lo eft,5^horizotauno pundo contingens.Tos tus prætereafub terris merfus,intra quem fi ta as d ftra

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dra fempernobis occulta manêtMaximus au«?; tern ex quinque mcmoratis circulis eft æquator, deinde tropici. Minimi uero(quodadnoftram habitationem dixerim)arâici. Porro hos circa los, citraomnem latitudincmintclligi coucnit, rationecognobilesexaftrorû fitu, amp;nbsp;coded 105 ptrgobaitUjSx^noftro inteUedlu delmcatos.Scn fu enim unus lacteus difeemi in ccelo potcft,re* liqui omnes rationed

S C H 0 L 1 A.

Otfi^ui.) Vteßctrculus CGDH,deijuopoßtriuidicetttr, Aetjuit dißantes.') Sumptocircinopes dusalterßatuaturin A ud B polum,al3 ttr exttndatur adaliijuamdißantiam ah ceejuacore C E D F: quern fic deferh hi circumfpharam continget.dicimusieqMdißaMem. Eiusgenerit tantum quintf affumpfit Proclus, quälet defenhi contrngit perfigna Ufa-Hex Apo h.es-perC O'S ex B polo.o-pernPexpoloalterutro. Septentrionalts.') Statuatur AB fignum ad quamUhet dißantiamex V uertice uer/ut M ho: ri^ontitfta-percircinißatuaturin B polum,alterextendatur in S contai ilumhorisiontites-fphterie.cumeaextenfionedefcrihiinteUigaturcirculut perfpheerä: neßfeptentrionalnfecundu omnem conditionem Prodi defcrii ptiontt. Intrahunc.') Sicmagitpropriedixerimutquammhoc,utuulga ta exemplaria legunt.intra hunc,ncpe feptentrionale. igiturfignetur quodt übet pun dum fupe' fphara propiut adß ,quamfit S fignum. c? uoluoi turfphara mßarmotutdiumi. idempundumapparet femper kuatum to» taconuerfionefuprahorix,ontem. HiutcircuUrecentioret nullam faeiunt mentionem: ueteretueropracipuamrationem habuerunt. Meminit huiui Strabo proxime initium operit de ft tu orbit: uerba eiutfunt ex Cali) Calcai gninitradudione. quodautemadurfatextremitat attigua fitoceano,fic innuit de urfa loquent: Solaip adoceani déclinât balnea nvnquam. Per un fam enim (3- plaußrum, ardicumfignißeat. Netf enim quorn tot ßdla eo la co circunferantur, femper perfpicuo folam dixit balneorum expertem oceat ni,netp ade'o eiut imperitU redarguunt,quafi unam urfam pro duabut agno uerit: neq; enim confentaneum erat, nondum alteram in aßraafeitam. sei' n quo Phanicet notarut, Cj-uffunt ad nauigationem, huncquoip ordinem ad Gracot perueniffe:ficut (3 Serenicet crinem amp;nbsp;canopu heri cj- nueüutter tiut denommatu: multatq; ad hanc ufq; atatem fine nomine manere, ut etii. ait Aratut. Non igiturreuefcftbitCrattCSolaaittemexpert eßbalneamp;riquot;,

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Von fugtendafugent.cómodtor Heraclitus,çrVomtroaftior, firnißter fro nrüico urfom af felläs. Aurorit mim er uefftra termini arâlos.ideji.urfa. It contra,urfa terminus fermi loMÏi. Aräicusmim occafuserortustermi tMts eu,non urfa. Per urfam nuidem,lt;iuam er flaußru uocat, cz Orient ob» [eruare dicit, arfiieu mteUiÿt. Per oceanû autem horisiontem, in ^uem, er ex quo occafus er ortusftunt. Diet nt aut iff urn uerti er expertem effe occa» ni, nouifje cognofeitur qubdadftgnu maxime arfiicu borij^otit eß arHicus. Confequeter itaif buie foetieu illud accomodantes, borijiontem ^«idem de* bemus accifere, quad terra: uiemu efi oceano : ardicum autem, quod terne nttiguum.quafiftgnu habitatiefartismaxime ardicum fecundumfenfum: quare er banc terra fartemoceanus alluit. Hdflenuj Strdto, eruerboruil* uusfere hac e/ïfententia. Cum enim m hocfttfermone, «t afjerat oceanum circunfundi ubitf terris, ne cut quod adfeftentrione quotf circunfundatur, in dubium ueniat, confirmât fententiam carmine Homeri ; Sola!f adoceani decimal balnea nunquam. Cuius fubmdefenfum enarräs,mquit,Poctam lo ^ui de urfa nwiori. Per earn dwtem figiificare circula ar die urn, per oceanu autem heriteputem, infra quern ardicut non defeendit : ficefuerhis accom* modatisfuo argumento.fufremifententiam infert ad modum hunc. Poita nonfuerit ufurus nomine oceani pro borixonte bie, ubi non or eifere urfam dixit, nift illtc effe oceanum mtellexiffet. Igitwr eß oceanus cum abjs mundi partit, turn hocetiamcarchne feftentrionalicircunßuus terrii. Hdc fum» ma fententia eß, n«nc uerba eiwi loci farticulatim exfendamus. Ne^ue tnim cum tot. ) Strabo exfonens urfampro ar^lieo.ne facerecoadius uidea turcaufam fui fm(us,reddit in modumhunc Poeta, dicens: Solaadoceani déclinât balnea nunquam. non potuit inteiligere folam, nemfe urfamexfer tem oceani :tot freetercaßeUis in eodem tradu cab exfertibus oceani.

Ne^ adeo.) Dua funt urfa: maior, qua Cynofura: minor,qua slice: hac Craci, ilia Pbanieei funt ufi in naMigationib. ^Mo4 Owidiui teßatur in Fas pit; sffeduasardos,quarumcynofurafetatur sidonijs,sheenGraiaca rinanotât. Elire eß froximaatrtirimundi;immô«jui polui uoraturexißit iniUiui corfore, eßefreliquis aßerifmis borealib. longe elatior fufra horia 3iontem,deinde Graru notiffima, folacf obferuata in mari, ob quas res foß {itquiffiam {quod er Crates facit} fuff icari,Homer a earn fracifucnotaffe illo carmine : alteram uer'oficuti feregrinäneef nouiffe. Hocre/ellit Strabo M^uient.'Nemo redarguit Homeru eiui imperitia, ut una tantu urfam noue Tit,cumduafint,ne.fquiffiamarbitraturCynofuramnonduferueniffe a* täte Homeri ad Graroi : immb ex ijuo tempore pbanirei earn obferuarunt, if fa a Grarit etia releriter cognita fuit, quomodo at ate nofira Bereniris eri nil. O-canofusßella annotataheri Cnuius tertius ab Aegyptijt : ad Cra coi quoeffere perendie peruenerut.Sie Strabo fatisfacit pro aßumfta exfoß tiene. Mu(tat^.)Ne alien« i/iud uideatur.nouai denif (lelias annotari.in» d a ^uit,aua

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^uit, autort et tam Arato citato in teflem,haud quaquam omne’e amutnera tai hafienus effejmmo reftare ad banc ufque ittatem multas fine nomine er obferuatione. Aurora: er uefpera:. ) Denotat bominibus ipfos ortus er vccafusfidcrum per uices, qui ceffant effe m circulo arâteo, ut Proclus mes mor at,er nos in organofpbara oftendimus-As uidelicct,er non urfa eß pros prieterniinusfereni \cuts, fuit aurora er ueßperte. Quod Urfa aut ë eße dut terminus dicitur, boc adeo eß, quod bums nomine Homerus utitur pro an {iieo. Orionemobßruarcdictt. ) Quit bodte aßerifmusuocetur Orion^ uulgatius cß quam ut conueniat admonere .• uerum is dißat ab urfa maiore per fuperfciem call partibus non minus lx. cireuhmaxtmt ,quadißantia facit,ut de boc aßerifmo loqui Homerus non potuerit, quafi bunc urfa obfer uet. Sed Bootes dicitur eußos urfie,unde eß illi Ardopbylaci nom!. Etbunc effe diëitim àplerifp orionem, autoreß Hefycbius in dicHone: aptair avrufn» kA. as^püp/ iigt;Tiie-.s öi'ofiaßrai ßeurleu: id eß, Orion,conßitutio ex xxUij. ßcls lis,quemnonnulltappellantBootem. Exbuius autoritate fentio Homer urn ftiborionismentionedixiffeBootem. Adfignum.') Maximearftteum, id eß,dtcens urfam uerti er eße expertem Oceani: intellexit fignu non quods bbetboriizÓtis ,fedquodipfius eß maxime boreale, utpotequodnos in fpblt;t taoßendimus eße in communi cortadu eins, erariheiapud S fignum.

confequenter. ) ideß, badenus de urfafiue arëlico, detp Oceano fiue borizonte diximusfecundum caleßem fuperfciem.Sed bac ut ad terrenam accommodemuSfdicimusboris^pntemdebereaccipi in terra fignum,oceas noattiguum. Ardicumuero fignumtßudeiusbabitata, quodmaximead boream accedit. Pcrobfcureauteminnuitfubuerticaliapunëla,er fubuers ticales circulas, qui in terra defignantur ex perpendiculo fimilium in calot idquodingeograpbicistraditionibusopportuniusdeclaratur. Poßlongant dißertationem Strabo redit ad captum initio fermonem concludens : quare trbancterrapartemoceanusalluit. Verumnospropter uniusardiciciri tub mentionem ad banc uenimus longam digreßionem. Porrb is circus lus A) Stella qua à priori pede maioris urfa defcribitur, radieem babet ai atatem Hipparebi gradus xi. Minutias primas v. cancri. Latitudinemab ecliptica boreale gradusxvij. M. primas xy.fecundu quam radieemfi infeti bitur in fpbaram ,• ifd ut eius ratio poßerius tradetur, reperitur declinatio abaquatoregraduumcirciter xxxix. Leueturergo B palus fecundumtotis demgradusfupra S bori:tontis,circulus'eparäicusperhancdißantid B 3 duet intelligatur circumfuperficiemfpbara: qui fic duÜus fuerit, ibit pet mediam annotatam ßellam, at que idem ardicus cenfeturfecundum aßumt ptumProrlichma. Haccaufafuit Homero,ut Utereturpromifcue urfaprO ardico. siquidem fub fuo illius climate cum ar diens circulusper partent urfa ranfit :tum urfa parte fui ardicu defignat in climat e,quo is earn obfer uationëfpbarafertbebat,quod fer'eactïdit terra Attica,et urbi Atbenarui

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Solßhialit.} ideß^iutixR polo.O’txtenfiontZ G pt^fpharamdeferh ptuseß, lAmÿlftmta.') Statuatur fphttraadalßumptupriusclimaAtht» Harum.solßitiaüs partem [mtórcunferentiit maiorem habet fupra heri^ea Uin. Per ^uantam ergo portionem cum fol defertur, prolixius curfum conß» tu,quam aliquo alto ecliptica loco uiemiore aquatori : rurfus nodéeeleriut perßeit, quam fub aliquo alio paraUelo, quoniam partem fut omniu reliquot rumbreuilfimamhabetfubhoritionte. Acquator.} ließ, quiexalterutra polo A n fcrtbiturmedtusfphiera.uteßctrculus C B D F. Hrumalis,') It eß qui ex A polo, er extcnfione A H deferiptus eß. Antarflicut.) Sta» tuatur circinut in A polum, pes dus alter extendatur in cotadum fphiera o’ horis^ontis apitd M fignum, circulus qui inde defaibi intelligitur per fpha» ram dicitur antardicus,aquidißans reliquis memoratis. Tarnen feptentrio» nah aquidißare dicitur à Proclo, quoniam duo hi ex part conßant aqutlata» tione. Porto hos.quot;) satis liquet exprafenttum deßgnatioue aquidißantes memoratos, er omnes circulos calefies carere latitudtne, efieîp pertenues li neas.Porté infuperficie calefii,netpifiudhabent quod forêt adeummodum manifeßi, fed quomodo femitam monfiramus in aéré uolucris prateruolan» tis,iino quomodo paulo ante arêlieos imaginarios delineauimus perfphard: to modo quoshbet circulos in fuperficie cah deftnimus phâtafia,exfiato tran fttu afirorum fub conuerfione diurna. Ex afirorum. ) Afirorum fitus efl locus cutüfquefitus in dtfiantia certa ex aliquo a/fumpto pundo. Sicut quoi erion efi aufitralis à uerttee, urfa autem borealis,quahs fitus certe oeuhs dt» prehenditur, Diop tra.') Dtoptraefiregulauiforia,plurimaparsinobfer ttationibusafironomicis.inhocuero organoaculeusereiius in fummafpit na,quadrantis habet locum er ufum dioptra ,ut de ipftus ratione pofieriori loco rurfus dicemust

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eVR QVINQVB TÄNTVM AEQ,Vli dißantesin fphara.

QVinq^ucro dutaxataequidiftantes dreu* 11 deferibi in fphaera folent,quod tarne n 5 eo ualet,quafi hi foil in mudo acquidiftates fint: quippe cum fol quotidie æquidiftan tem equa^ tori circulû,quodlênfuanimaduerti licet, mun di rotatu peragat,quo fît ut intra circulos tropi cos centum Ixxx.bis circuli paraUeli à fole deferi ban tur. Totidem enim dies intra reciprocation nes numerantur. Quin amp;nbsp;fteUæuniuerlæin agt; quidiftantibus circulis quotidie feruntur, non tarnen bi omnes in fphaeram adhibêtur.Quod tametfi mulusalfjs rebus in aftrologia condun cant,fiquidcm fieri ncquit/utuel afitraprobè in fphaera

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fphæralocêmr fine omnibus æquidiftantibus arculis, ud examuflïm dierum noÆnincp mas gnitudines fînerjfdem inueniantur:tamê quod ad primaaftrologiærudimenta non adeo utiles exiftimati font, paru uifum eft eos in fphæram aferibi.Quint^uero æquidiftâtes circuli ob eer ta compendia, quæaftrologiæ tyronibus afFes runt, optimoiurein Iph^ramfuntadhibio.Scs ptentrionalis enim,aftra quæ nobis perpetuo eernuntur définit, folftiualis tropicus folis recis procation cm continet, finisc^ eft eiufdem in bo reâ tran fitus, equator drculus æquinoéria corn plcÆt. Brumalis tropicus folis ad auftrupros greftî metaeft,ctbrumalêeius reciprocauonem in fe habet. Antardicus drculus,aftra quæ nos ftrum cÔfpedum fugiùt déterminât. Iraq; cum his qui primis aftrologiæ rudimentis imbuens di funt,ccrta emolumentaiuggerant, merito in fphæram coniccras quis dubiteu

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qiiodtatnen.} tocatoenimfoiefubcjuocuniffundoecltpûct C CDR, cum eo loco exiflens. cireuferatur per fuperfleiem caU conuerfione diurnes, intellignur ex illo pudo defgmre aejuidsflesntem eo exemplo,lt;juo exiflens m «rilfrurrofigno G uel H.deftgndt ecquidiflantem (jni tropicus dicitur. Quo flt.) üenda eft in numero. Rij fnim f xcij. fdcii ccclxxxii^. ejuot dies in an: no.amp;integraineclipticapundanonfunt: legendum fiierit clxxvj . Srewn» Jumenra dies anni ueteres adnotarunt, aquidiflantes lequatori fatis probat bill ratione, tjuod totidem dies intra reciprocationes numerantur. Hedietat um autemaflumpferunt, quoniam quanto numero dierum tranfit a tropico inbruma,tantoreditlt;ibrumaad folflitium,\ntelledusefl autem fol defk gnare^diebusfmgtilis fingdos paraUelos aquatoriinflar fummorum duo* rum,auiftmtadfoljHtiumctbrumdm,exG o- H flgnisdudiperamhitum^ Q^in à flellet.') signetur enim quacunep locofpbeertt pundum tanquam flella

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fu «quiJipdntium.

VErum ex memoratis quînep equidiftâtib? circulis, arcticus fane fupra terra totus exî ftitSolftitialis aût tropicus,biparti to abhorizo tefeindicmaiore eius parte fupra terram confpi cua, minore fubter occulta. Ncq; tamê in omni tradu,urbéuefimilitercirculus hic ab horizon te fecatur, fed pro climatum uarietate,uariam fe« chonû exuperantiâ fortitur: q s quocp,qui pros plus fep ten triones agunt, ingquabilius ab hori zonte fcinditur. Nee finis, donee co loci uentu fit, ubi totus fupra terram emin eat. Qui uerb ad auftru magis uergunt, fi s profedrb per inæquas biliores partes ab honzote diuiditur, donee ad plagam quandam uentu fit(nobi s certe auftras - nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;e lem)in

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lern) in qua tropicus ab Horizonte per æquas partes fecatur.Atin n oftra habitation e,itafolfti tialis ab horizontefeinditur, utuniuerio circus Io per odiopartes difledfo, quinq^fupra terram appareant, très fub terra latcan t. Sane ad hoc di ma direxiiïè ftilum Aratus uidetur, cum Phar# nomenacolcriberet, in quibus cum dcfolftina^ li tropico difierit, ita ait:

Huius in oclonis diiTccli partibus, alta Terraru inuifunt quinq;, très ima fréquentant Alterni amp;nbsp;Phoebi reditus celebrantur eodem.

Exhaediuifionefequiturmaximû diemho# rarum gquinodialium quindecim efle,no0:em uerb nouem. In Rhodio autemhorizote ita tro picusabhorizonte dirimitur, ut cumcirculus uniuerfus inoPto Sd quadraginta parteis fecet, undetriginta fediones fupra horizontem appa reant,undeuiginri fubterralateant. Exquadi# uifionefit, utapud Rhodios longiflimus dies, boras gquinodiales quatuordecim habcar,noX nouem, additis hinc indefemiffibus unius ho# ræ fingulis.Æquatoruerb circulus, per uniuer# fum terrarum orbemita abhorizôte diuiditur, ut fcmicirculus eius fupra terra extet, femicireu# lus fub terralinquat. Quo fît, ut in hoc circule» æquinodia fiant. Brumalis aût tropicus eara# tiôeab horizôte interfedus eft, utminor c fedio nib. fupra terra habeatur, maior fub terra. Inæ# quabilitas uerb fedionu «andern in omnib. di#

matibus

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SCHOLIA.

Nf^tdm«).) LtueturtnimBfolus/upra S horoiontitperpun^a, uh pott xxx. Solßitialis maiorisfutpant ent fupra hori^ontem, Uurtur B po lus ahiusjolßitialis item amphoriadhuc fui port tone quam fuerat, primus eritfupra hori^ontem, boef iUi continue acctilit magis, quo magis leuatuf B polus.Sic tandemeueniet,ubi B polusitaleuabitur ,ut circtdus du flut ex L ueneritfub V uerticem.qubd fotfitialis contmget horizontemapud S, totusergoapparebit. (i/iiuero.') Videlicetpopub quimagisadaut firum conctdunt, qu'am bi quorum nuncfitumfpbane exbibuimus bis, (re. t,rgocÓuertamusfuperioraexempla,(r B polumdimoueamuscontinue ma gil d uertice : erit quoffolfitialis parte fui apparente aquabibor, continul einonapparenti. Donecad.y Eaplagaeßfubaquinoâialis,fiuefitus fpbararcfla. Demittaturitaf B polusuffin S borit^ontis.uidebiturfol» ßitialis partib.fuis aquis effefuprafubtus'f bori^ontem. Ex bac diutfioz ne.') SolßitialisintelUgiturdiuidiinßarxquinofliahsmpunfiaccclx. qua ft multiplicentur in V. partes: uiddicet folßitialisapparcntis, (rfumma di uidaturper viij.totameiuseircuferentiam.proueniuntpunfla ccxxv.tlac diuidanturperxY.unamuidelicet horamaqualem,proueniunt bora diet ma ximixv. tioflem.) Secundum prioremrationem partes tres non appat rentisfolßitialisrefpondentpunflis cxxxv. tiacreddunt boras aquales ix. Kac quantitas diei maximi (r noflit minima accidit in climate Atbenaru: quemfitumreprafentamuslt;ifpbara,ut AEfignumdtmoueamusex Vuer tice uerfus M, per partes circiter xl. Cr femis. In Rbodio autem bori:ï,on3 tf.) Suffecerit prius explicatum exemplum,pro boe quoque loco exponcni lt;lo. Po)ïfri«i tarnen canon dabitur in uniuerfum, quomodo maximusdies ex lt;14 0 climate,uicifftm ehma ex dato maximo die deprebendatur. Erumat ^tü Haebabitudomanifeßaeßexfuperius enarratis,exfinfpefliÓefpba ^ic: quare nulla caufa eß,ut circa earn quof oceupemut.

Ptex (ci'yeSiss Tant Tsr^fTSt 7^«^nA®p KUKÄtep.

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Tit^ûl/ Jè w cùjTKfuyi^H (iiTct^n-sifa i^x^k w K.Âl(zet7ety Kf OISp^/xâ^cvt^^ois 5 thiXT/otftSh- et WK^t yivovroU. oï /\ y^ ‘foTTlKoi WK^l^ H^ 0 la-Hi^i^iVOS Raff’ ohlw T^ OÎKOVfjJÜluJ i(èt ôiri vgt;is inybdurtp, oi af^ XfKTiKoîy (^iram-^ova-i \^ rie lü' yi^v, jlt;^ ois (J^ t^a^vA-y ois lt;ff^ ihà'ifovib- yivovrou» S?f /\ yoî^ TT^S oç^K^^ oiKOvirt /xét^dfiib' 01 s^KriKoi KvxÀst yivovi^gt; quot;nS) yo^ wôhv i^iTitO^OTfffÿ (f0UV0(MVy cu/ocyx« 0 quot;^IZ 0^K7l Kop KvxÂS(/ ’np z(pci^ô(jffin'op Ti) o^t^ovTos (iffi^va «a (jtaÂisd yin^oa. rgt;is tff^ Îti Ti^s ix^'x70[/oixiert ytnTca to-ôtè 0 3ifi' vos Jgt;omxos XVXÄSS K^XTlKOSy WSTiCÜsJ'vOKVKÄJSS ttflX^^tÔ' trou. à^H^is “^iz 3^^tviiz T^OTTixop KyxX9^, t^ -niz k^xTixoiz, Hgù f^ictij (dzxÂaffêiy Toi^ip, tt^s 'j nw oc§K7txo7fffovs roTriSSi i(aù 7lSgt; 3i^tVÿ fiOTTlxê KVXhÿ /JlÔi^OV^ Ot K^XTIKOI XVX^St yl VOIZTTXI. TSTi^XS o^t ^yû^tlt ns w^f a^x'^iz Xlt;llZjiiH yÿvx 0/\ Tffo^S xane xo^viflàz yiviTVi. 0 efî K^xnxis xûx^ss T^àz tÛ ift^ovns Z7nyamp; mi^iiz, ly icfta^fzó^ outS izir« tIz^ spotflin •r£gt; Koa-iiÿyff^ -n aù'^ (iiyiSos Âxn^euzs '^ îtrÿfuptv^yûs^i OÎW fàs XVXhaSy quot;^If X^XTIXO^ K^ r^lz\a-HtliflV0lZy1(^ QO^ Oÿl^ ^ovfa 7^ cÙ/tÜz TK^ip i^ âilt;rip ^X(j.^côzap. ■tsrdhuz lÆ 90?? Tr^S tuo-f/ixëptxiz olxStrip, of pSji uro^t raTT^vón^oi yivovroUyOi y K^KTlKoi XVxKSl ihdo^OV^. K^ TSi^XS ^^ TtS^X^X TT^S lzt^' CHlx^^tXp »/iSl[Z KCi(Mÿ,!idn 'n A è^hp « Ä^yOpiSivH VW) T Îx» Izt^i^ivà^z, ^^0t (jJi^ Tirö^t \^ 70^ Ô^l^VTX ytVOI^ , ot Jè X^' KTIXOÎ xûx^si xxd' ahv OWIU^OuZ-Tf , S)S7i CUZ71 7 Tff^n quot;lirX' ^x^Kh^ch^/ xvxÂuizfàs 7rx^xXlt;tt\îss yiVi^y ms « T^omms ifCU7^^ix^(^i^li'0p,

DE MAGNITVDINE JEQVlDISTANTÎVM.

SEd ex quincp iam memoratis dreuKs, quo« rundam magnitudmem, per uniuerfum ter raru orbemeadê fibi conftanqnonnullorûpro climat! bu s mutantur,alfjs^ maiorcs,alqs mino res circuli euadût.Tropicf em'm Sff equator pa# res per totum orbem magmtudines feruant. Af

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^licimagnitudmecuariantjcum alibi maiores, alibi minores cernantur.Quippehis qui fepten triones uerfus degunt,maiores feptentrionales Hunt, cum polo magis in altum fublato ardticû circulum,qui horizontacotingit^necefle fitaflî duemaioremfieri.Hisuero qui magis etiamad fcptentriones uergunt,interdum folftitialis tros picus in arélicum plané abit, fitq ut duo circus li feptentrionalis, tropicus^ coéant, pro unotç habeantur, adeo cü magis adfepten triones etia acceditur,maiores folftitiali tropico feptétriona les redduntur.Nec finis donee eo uentû fît: ubi quoniampolus fupra uerticem confpicitur, fes ptentrionalis in horizontislocum cedit, eiep in mundi rotatu côiungitur,æquatoris plane mas gnitudine,fitcp ut tres circuli,feptentrionalis,æ* quator ethorizon,eundem fitu pofitum^ obti neant. Rurfus autem bis qui ad auftrum babis tantpolibumiliores fiunt, feptentrionales uero circuli minores. Finis aut decrementi, eft locus adauftru nobis fub æquatore, in quo polifub borizontebabetur, Septentrionales autem cirs culi prorfus euanuere:ita ex quinep æquidiftan tibus très denicçfuperant,nempecumæquatos re,tropiciduo.

SCHOLIA,

Cum polo.) Dneimur tofietcirciJumdrfïicumdfffrif’iM B polo,ö di« Jîiintid dd s ftgnum bori;(ontit.Sf qititur.Ht ^uo cleuattor tflpolus.eo fa mi iordi/JdutidB SjO-nMioreirfttlM.^uif^tmrtioridf/critifBrtxten/ione.

» nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;' nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;e » Hii

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Bk um.) A.clmoueaturfphnera in L punäo fub V utrtieem.ciTculus tu 8 S dißantia deft^atus pro ar^ico, idem mcidit in ipfum folßitialem, eßlt;f is pro arélico. Adeocum.') Admoueatur B polusuerßu V uerticepro* piusßtupriori arcus B S.euaditamplioradhucproximoprioredgitureiii aräkus E S euadet nie maior priorifolflitiaU, N«ßnis. gt;nbsp;Admoueatuf, B fub V uerticem, cripßiexemptaeuenkntfijueehicmemoratProclutmiß quad rü tret modo,fed omnino quatuorÇnam tribus additur ont ar (Heus') eun aernfttumhabent. Rurfusautem.') itisquiadaußrumhabitantAntelltge non qui ultra iequatorem,fed qui habitant außrahora his,de quibus medo di dum fuit. In quo poli.)-Sub hori^onte habentur,uidelieet ineidunt part* ter infuperßeiem hoftsiontis apud illiusfigna M amp;nbsp;s.

n^t XfiSptÿ 7wp/ •^x2AHÂuy,

amp;.iKya^ “^ '^oa^9[eSljvx ov^Q^aKH'sifiii/ KxSohiKÔis yt' tnôtxe 7gt;ùs tffiVTi r^xTiKuhavs, à^’ us 7ramp;s rbb HixiTiÿxif eÏKutrti/ 0« ttKhSos xjjTÛptKKêiâ^.^ert yx^ Tivis 'o^t^ovTdb-.,r^ 0tsJgt;ôs pûtroi tffX^ÛTiKHÂtt yiuiufeu KuKhot.aa-t (/^ oIkho-iIs ùâï TUS yùSy ^(^ Tr^uTÿ pSir oiKHO-is, tssx^ ofs « Siftvàs tjoottikoS KUKÄ^' tlfX^iTCU 719 o^t^ovr®'., Si^i Tup TjP X^KTIKV ItV' KÀts TU ftp hxp^ewet.ifdïi'n.ÿx lt;/è 0tft9a'tS^H hstyopSarH y^nso ^ tSrihUp.T^IT« t/é èf^p OtKtiXlSy VWtg »S ptK^àp VSiÇOp à^HM' (Jljp^H oi^iirxyaÿfbapStj^ÿ varâ Tep ia-Hpi^tvip,

de NVMERO AEQ,VIDISTANTI VM, NEc^enim obea quædi'éiafunt, quinque perpetuosæquidiftantes exiftimandum, fed pro no lira habitationenumerumeoruexi^ fiere: quippe quibufdam in horizontibus, n'es duntaxat æquidiflantes inuenias.Suntfanè ÔC fupra terra habitatiôes, quaru prima eft in qua folftirialis circulus horizontac0tingit,ctpro ar di co plane habetur fecuda,quam fub polo ap« pellac T ertia,dequa paulo anteretulimus, qua fub æquatore nominanu

ptji

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Vi^i TKfuûs'rîip’v^n z^et/tiH-

Atop xvxAttp»

câiy »y « rà^tt quot;^p n^Ti TSntpttlSiHÂUl/ KVKÂUl) « «VT» wag« TSKCrty lt;f^^^ K^’ y/ (jSiji' TH Kxy HttKS olxXiAvH , TT^, -n^ (J^j^ cyoïiO^Ttu àgxTzxûÇj/iïbTtg©- Jèy é 3if très 'rp67rt^ KOSi^X îirHl/.iflV0S,gt;^}(^y.i^ivàS-, 'Jffiy.y^©' lt;/è tWTK^KrtKÓs^ 7015 J •!Tf‘0S (C^KTOp /4(ê^9j/ »/xiy 0tKVlt;rtif.,yivit7tU. TBOTt 7I^Si 7ûi^ 0 3i^tvis TpOTTlKCSy /lV7ifOS t/^yi K^KTIKOSiT^trOS l/it 0 ia-H(ii^tvo{.f m«^7DS t/è^i eÙ7X^K7iK05^TiriiJi';ifamp;‘ Jlè^oyetin^ ^tvis TpOTTlMS. TS-X^ 015 yc^ 0 «pK7lKit KVKÂ^ liftîfiip yivi^ 'm Ti^ 3i^ivov 7yi97riK0v, K^a^xÿ tIm Tri^oi^Hpilj^bjJ 7K^i^ ÿxnèÿfai/'

DE ORDINE AEQVIDISTANTIVM.

QVo circa,nec ordo quincp acquidiftantiS circulorum idem apudomneseft,fed in noliro tradn primû fine feptctrionalcm dixe« ris,fecundum folftitialem, tertium æquatorem, quartum brumalem,quintum antarcticuiri. At his qui propius quam nos feptentriones incos lunt,primus interdû folftitialis tropicus nume ratur,fecundus feptentrionalis, terrius æqua« tor, quartus antaróKcus, quintus brumalis cir« culus. Cum nanqjfcptentrionalis folftitiali cas patiorcuaditgt;necefleeft memoratum ordinem feruari.

S H o L I A.

Summafenuntiaeß, inter circulot arflicumo-folßhialem faéia colla, tione,alter alteŸo cenßetur prior,ijui amplitudme fuperat. Eurnit aute quod aräicifint minoresfolßniali,donee uerfusfeptentriones perueniatur adfitu fpharx eum,quo folßuiaHs totus emer^it,izrfa idé qui arélicus.Etfi B polut propiuf

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froplus hocfitu dduertlcem admoueatur. Xpfe quotp arâteutfit tnaior folßh tialifCr numeratur proximus ab aquatort, exempta haru prius txhibitafunb

Pi^i i/luu«{xi6ùs quot;rSi/ -tslv^ ‘^xXKHhuif KVKÂapf»

ô(xotus cfê v/' xi tâuuxixeis TZp/ T^t^n TsrxfxXKHKup àv Khaip tu MTcu ^aty. a yc^ ttx^ Hixtp SiftvosfoTriKos KVK^St vis xiTiTTOini/yeixi^iyis 7pa7riKis kvk^@' yiimxu.b j ttx^ tK^VOtS Si^tvis f^OTTlKCS KVK^SSj TffX^ »fxip yttfiTtlU yilxi^tVCS JiOTTlMS* quot;^oTs lt;/è VOT TOp ta-HlXi^ttfOp OIkSiTI, TH (J^V (/luxJXlxd oijgt;êis KvxÂoi Si^ivoi atri f^aTriKul. ■^^ Mriof yc^ tÜj Tm^a^ t/lop Tii hKih kSvtdu.th t/è 7i^s x^H^vs “^^xX^xyu y^otr xy Siÿtvàs /jXv’ßoTTiKoSyb Tffx^»iùit tlt;rH{x.i^tvàs. yi/xi^ivat tÆ ai t/lvo TÿOTTiKdi.tpvtrf yjÿ AtyoïT «p i(^ KxâohiKSis 7r^s X7rlt;X exv tIiX) 0tKtl(Mÿp ai^tris T^iTTlKOS KVX^OS ^X^ylpyO iy^f' SX Fï oIkhxuds v^x^ytep.^ /i ^p turixp 70Îs \^ t Îa-Hpift' vop oînovirt âiptvosJgt;O7rtKOS ytviiy b la-npi^tvis- T07i y^ xî/^ vis ^ ào^vtpbù ylvi-nü. b »htos.îxHixi^tvot cfè ^vK^9l ytvait “7X1 Tirx^ cùfamp;is tffw/TiS oi •:^x^^st. îtrÿpi^ixyc^dj^ ttM' fis dh ntx^ cùxTois-^t'Tis yc^ oi TffXf«JiKn\ai û.vt(Âst J^iyp' vp^vTiu rgi o^i^vTcs»

DE POTESTATE AEQ.VI DfST ANTIVM.

IAm liera nec poteftates gt;nbsp;corun dem æqiüdî^ ftandum cædem. Nain qui nobis fol (b rial is circulas habet, Anupodibus certebrumalis effî citur,contra qui illis folftitialis eft,nobis bruma lis reddit.Sed qui fub æquatore degût, his unf uerri très circuli uiribus plané folfritiales fiant, utpotefub ipfam folis orbitâ incolêtibus, quart quam fi adfeinuicêconfcrantur,qui nobis pro æquatore fiaaritur, folftitialis uicê obtinet. Âm bo uero tropicipro brumalibuscenfenf. Nan# que is démuni natura folftitialis circulus perpe# , nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;tua^

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petua^rarione in toto terraru orbe dici poteft, qui proximo habitationem habetur. Quo fit,ut ps,qui fub æquatore agut,æquator ipfepro fob ftitiali ftatuatur, utpotein quo fol fupra uerucê agitur.Pro æquatoribus autem omnes æquidb ftates circuli,uelutperæquas partes ab horizon tedificcu.

SCHOLIA.

Solftitiaïem ctrculum, uocat Produs omnem aquidiflantem ai^uatort medium inter duos tropicos:m quo fol ad diem ext fens,incedit per uertieem fuliedceregionis, ut qui per initium tauriparallelus ducitur, ef folflitialis habitanttb. Heroën infulam. sic uocemfolflitialis ueteres acceperUt: quern illorum ufum qui non aduertunt, non facile explicabunt locum Lucani: R4» pidifleonisfolflitiale caput. Antipodibus.') Antipodes dixit bbertus eos habitantes i regione,0' ad au flrum tantum abfunt,quantum nos adfeptens trionem ab aquatore, qui Antaci proprie dicuntur ; quibus tandem qui Pet tiacifunt.^demnobis uere Antipodesexiflunt. Hampdemum.quot;) Mac rd tione qui per cancri initium parallelus ducitur, idem cenfetur folflitialis du plu i rationc: Superiori,quia imminet his qui syenem,attp alys periacis qui idem clima circuhabitant. Deinde hac peculiari,quia regionib. borealiorib. Syene his efluiemiorm reliquis aquidiflantib.

Pi^ eflixsxaius ■? tfft^n quot;^x^AhAcop KwAap, où e/è dû c/lixsKcrGÇ où KTT «TAuAap Tois KVK2^i5 cû cùncù t/llXpSiivai Käs' cALu T^Ù OtKÎSpSivbifiKTAK TT^S /J KXTX^CC çbh ^ a^eufoip tfiou^ouZyf Snes.'rei ttsewns pno-HixS^ivv av KAVt/luU^tSpSlvVeiipifp f/oOÇfllTiKBgtC^'Tÿ'tffÔAit Kxfxy^x eJUTOU KTTe^Oip ff s» 0 (/''’ Cljù’ns U^ QKT^X fXi^H èCR ^ 3i^tuS KXT«y^Klt;p^ tTfiJ^ap ff 4.5 e/è îcTHpi^lvis Klt;^ tKX'n^OJp rwp quot;floTTlKajp ff ef, 5 3 X^pi^tvis IJBOTTIKOS KVK^S 0^ ^ eWTX^Kfi xàKSTtjl^amp;p ffi,lt;i Jècdt7x^K[tKd5X:^'ri)Tffo2its^fs. ^^nrdè' ^^ 3X*S*f'î’3 quot;^^^‘P ^ quot;^KS ciJU7«5 i/lixsxcr{s Ijfjtsxtp X7r «A-AnAbip 01 KVK7^i^x^ ai pSM J^omMt ûà ^ taHpifivS-,^^ 7Txîè tyKAipaT^ouiTlM xTrósxaipiy^tnp.oi Jî'foTriKii Kvn^st ^ T c^KTtKwp à tÛjù xjjtIÙj tytsai tfiKSX^tp-^i^ ttcwtxs oîù ooi

f ^Jt-TÂÎ

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F P 6 K A O Y

^ai^txStK^'oi /\ tAKiwaf/jö« 3 TrAaeiz /iïscclt;rii/, o/xctt»; 3 ai a/ KTiKoi «^ ■r TffôhuytV Thv Ïirbü kmsxlt;rtigt; t^vxt ^ Tstt^ ty' KÂi(Jia, «AA*aî ^tSCk iÂKT/'jii^oï cf^ TTÄfiäi. lc.«’rxy^«ifgt;ov'j^ [tSiv 'm ‘Brxlt;rM eu cepeû^cu Ts^s ^i^in tMiXo^/ io/^ovrx^

DE bNTERVALLO AEQVID I ST ANTIVM. SEdnecinterualIa circuloruintotoorbe à fc inuicc ftatafunt : ucrû pro fphærarû defend ptione, adhunemodû difpenfari folêt. Diuifo in fexaginta partes meridiano quouis circulo,{ê ptentrionalis circulus à polo fexagefimarû par« tium fcx,intcruallo dcfcribitur.IdeiTi in alteram partem à folftitialicirculo ièxagefimarûpartiu quinq? interuallo notât. Æquator ab utroep tro picorCi fexagefimis quaternisdiftat. Brumalis circulus ab antardico lèxagefimis quincp. An^ tartfh'eus à polo iexagefirnis (ex. Neep tarnen in omni plaga urbeueeandêintercapediné inter fe feruant:fed tropici ab æquatoreparem in omni inclinationediftannâ uendicât. lidem aûtab af élicis nô pare per om nes bonzo tas, fed alibi mi norem, alibi maiorê. Ita demu 00 arÆci à polis nó parein quauis indinarione diftanuâferuât, fed alibi maiorê,alibi minoréhabet. Sphgræ ta« men omnes ad Græciæ horizon ta ddenbumr.

SCHOLIA.

Proclut fach partionem a^uidifiantiumjecundum clima dufiu per Rho dum.Parttsenim vi. tjualiumeßfphitra lx. fupermaxima circunferentia ronßituunt gradus xxxvi.quahum eß circunferentiagraduum ccclx. niut difpoßtioeß AH fignu,mouetur ah V uertice contra M hori^^ontisperpun üa xxxvi. \demm alterampartem.) Secundumfexagefimapartitionent fphxrxjacitquadrantmttrx^uatorcmamp; B polumpartei xv. AtdißM Miata

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tiiiinWrf^M4torrwO'tropifHm,«t(a’m ê G part« üy. o-^tt4ntitlt;üf«= p€r4rf«meridi4niB S pdrtfi vi. Sitrgotirilicusdeft^tturex B S.dc-ff. ditdtropuumin Q adfortes v.Hxcabinfftfl'iont jfbaramultomamfe fiiwa babaur. Nf^ tdmen.) H4fcedt ergo drflitui nmfUcaufafub aUo fituffbitraarcum B s.mmortmpantunatiudliumfuïtbafltnusfarttum yi.DißdntiddtfO4dtropifMm,fjïp4rtiMm vi. Kurfusahofituhabeat3 S naiorempartettna,ut vÿ. Diflantiaabeoailtroficum.rtfitrieturpArtium üij. sirinreli^HOijuorunf fuu ffbitritrt^trttwiibtdamp;a.bd difldntid, und fexdgtfmdfdâtffddus yi.ciudiiume^circmfertnt'id ccflü,

P^ex àuAsugtop KvxAU(/.

A(K Twp TToAup «At ftcx [t.vK^i ysov rivuii Ló^v^oi ^oGe ^ogtvo/xStkflijflfj vvi£\SHK’ty ’«ob tov i/tuy ‘n^f^i^i^iwii tus OJSI KOa-HIS TBÓ2i9VSiJ^lgt;, UiKsV^Ot 0^ KiK^HTtU^cl^ QO ptfegj» TX «»K «ôtigÿT« cdnÙiij yiv^ä^, oî (jiSjf yetf Äai7roi kvkäsi y^ t^ vsi^tspolt;pluj Ttf Mrnv ólsi SttopoxóiTTajTip «Æ xöAsvgtop kv Khiefj in^ti rtvi Äi «fltigxT«, tk oc^ t/P «ù'TagxTXX» vcrè t oex^avT« i7roK(ttj£cwó(tSbf«. y^iepov'nU ’j outzh ox xvxAsx Jj^ 'rHni '^Q7nKSii/ {rvtJ^auy, KW es /xtg« A. ïQt /lou^ova-i TTp t^ lJt.wuy 70)^ ^^Kuff xvxAup.

DE COLVRIS.

SVnt 80 per polos dufti circuli, quos nonuls li coluros uocant .lis accidit, ut in ambitus fuosmundi polos recipiantColuri autem diéti funt, qubd partes aliquas in fe minime confpe« ébshabent. Reliqui enim circuli in mundi cirs cumadu integri cernuntur.Sedcolurorum par tes quæpiam, quæ uidelicet ab ardrico fub Boris zontelatent, cerni non poffunt. Signanturaus tem bi circuli pertropica puncta, diuidutep per du as arquas partes cif culû,qui per media fignis feriducitur. *

f * Scholia,

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SCHOLIA.

Signantur.y Alter amborum A E B F,uaaitperfiÿtatropica GH. Al ter A C B D fera^ttinoâiorumfigna C D. Re^qui circuli quihaélenut funt defignati, emergentes conuerßone cceli cernuntur per panes: fed colua rorum partes qu^epia, m^^uit Proctus.^u^eadantardieufunt.cerni non pof funt. Atquialiquofitumundicernietidhimtegripofunt. ReuoceturenM fphara infttum fubaquinoélialem, uteum alias deftgnauimus.Vtenp coins rus bis confptcitur,cum mcidut diurnaconuerßone infupcrficiem horizons US,femelmatutino tempore, rurfusuefpertmo.Quare Ptolemäus eos caßi gatius uocat: hunc euntem per polos oßgna tropica: ilium euntem per pos los erßgna aquinodiorum. Sed Proclus conßderationem habuit fphterana Ml umuerfum, fed eins qua ad climagracum^cjuod dixit fuperiusydefcripta foret. Diuidunt.) Srngulie^uidcmdiuidutfigniferum C G D H in pars tes binas,fed amboßmul eundem diuidunt in partes quatuor, eßip in Craca leihone A pro n legendum.

Pi^^ePteCKÿ itvit^SV,

Aofii (4fc àh KVK^9fjO T iS. ^eAÏupf,. tdiy^f j lx 'jplZfl KV Khcup •^xTAnAaiy trouAsKKe^ySip/ ot/^To tiAktis ie^ooi^^P yi-rf ^ ^(ofiXKÿ KVKÄ}s,i ’j e/J^(Àtrap t^ ^axfiospi KXÄS7f.,v^ efè iepXTÏfzTOU e/lvo KVgt;lt;Alt;op Ïa-üip ly ■^xAAÛAtupt^'nSi /\ 3i^ivi fo7nxS i^ tUt 779 hx^Ktuis quot;^inïju fiOi^xsry'rS) j )^4pti^tvSjgt;^ TTiKV i^ 7^1/ tt9 «z^oxtpamp;ïof Tt^inluj ptaitpxi/.gt;3 efè 5JA«Sf f ^axftXKV KVKÄV è^ (sof^ou. tS, Ksfes J^KiKÄHTDUO^t/ltXMf amp;.VK^S,lt;flk quot;^ T^ixv^jj nfu ':^x7iKHÄtss ^vxAisS^

DE SIGNIFERO.

OBIiquus circulus is eft, q duodedm fÏgna continet, ex tribus gquidiftanöb. circulis conftasrquoru duo latitudinê figniferi determi nan^unus per media figna duclus uocatur, bic adeo duos pares èC equidiftantes dreulos attin git, folftidalem in primacacri parte, brumalê in Capricorni principio.Latitudo figniferi cotinet partes xij. Didius eftaut bic circulus obliquus, ^ f qui Jtfütes ad in^quales angulos in terfeccu

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’T]lt;ii.ßO4XZV)t Stjn^ Sotd^t^ ^ tiSrmy,^ SuurS niiJi |^ z'CraC'^ oJSS^'Si'Coy xtti^n^iij} ^ dojdi.o'^v dt ài^xd A^if di^ SMio^i^idtj zJojimjiim^ev f^ ^'■^i^aai'x xjaó^iia r, fix /^dw^^imx àÿ^jm ilmfiirlotb’^^s ‘ Sn^n^x SniL ^ ^id^^ •■i5o »0 ei,40lt;l}X^^^VTj /W » 'So^mtsa. -^ àm/L»yfiigt;»tjgt; àt^sat. ^W f^^St^HdlJtX f3xnlt;igt; i^ ‘^^f^'i ^ O’öxudiv nrlxy^ is^ tit icAW t^ nJ^txbzSst^zjirfaj) ‘ àtxnygt; t^ ^ tlnyoziam ssiii Aoyunjt ^ it^ohlt;b ^f]2i,/ms!L ts^’^^Tt jouts^ \/ p no'-irTjim *»2 rntizm tj/gt; Smin^M spiL ^ âm^f^o C TnojLviixS^xziiiyt R*»5 C^Xt^p vdiflOAn)igt; )u. V^Aptso. 7^ »rhyH'(?i «^ r^'-à(^tJo o ßlt; ti/ptJiVJ^^ii^ltflxo'x ffi, So^^rl ilxdPWJiO ^^xn ^^'‘f'C ^o^o^xio. âxntii^ts^ xrix MxJi^iSvx ào^oy x 5^ ^ C. mxij 'ixnoH rto fiByuyfiX^ ^m ^ ^ 5^2 mMdox3 âtxxj^ xr/x Xp äx^zrl« x n ixzripyn. t^ tkXSx ioj, fq^il tv ’ xixu'^x^ x^oaw^ Xu, »t-f^sa. l^^af.rrx ax xrliyv C. op, '^5o^xi^ t^ '^^J^ ‘^ ? ^flfxaêKJxiss^ rlmij/ixs ^w^atI ÜV âixnoxw as^yfiix^ amp;i.rp) ^ ^ W S^iiL'flo^o^xJii, u/n3i^^figt;agt;vi tlczKi^ S^u, mpt. I^ xa^^^^iixyxtyp ^Sxi/vs Sf^lxlgt;^gt;^x^^ Sbibâ r^ Smxffmo ^ r^/Cx^f^x^ mpt. ^^ 101.^ npgt; *Bjfi}jf,xu,^fl Xd)[riod7xlt;b xu. xu.d^ 7^ ^zlmJziixtip» xrlryit lt;x x^xk txx^'idi'C zM^iSo so^u-i f'Sn'ixtfitio |^ f^^Xyf^x^ mjj. f^ äx^odt^ ämtyixs^ àx4 Çjiydi. 'äß^Xf^ Mm XU.^Xfqpl0d7Xlt;lgt; M Md^ i^^XiHYX ar.

^ànS^rlM Am H^^zrl m 7^ zsm ‘ jgt;^Xf^ ilm^f^ Ss^m o SfiotxonX'^yL 521^X3 ^ âo^'îKgt; zIjxh^tx mp. d^ S^if, X'^x *'^^}^h '^^ ^^^'P^ ? àtyoja. ^ âxSmX^ àxxxsa. i^ a '/lorlxttt ^0yp x àm7flt;^oXt^7^ ^àx-Hut^ 5x5mlt;l7Jgt; tlxhsx Sx-gt;,xx^oàmd xyiiX âM ^ i^yi o ^àf^ âx^iSi St^uSmp x'Coy Ç. a 'âniyt^i^p f^XJyiXS àp(^ à^dLzrfxt^ Jjx Xdi^firl p Sn^SmxxSo ^ àorlJXJ, vrlii-tO-üX àoi. l^ S0d^oi)x^ilt;ïÿ^ Sxz'f^o sx^^.LZ7f» i^ a^xx g àx^iSo àt^ dS dr^çr) SozS^m • Soz/idx7,ÿ X'Coy g ^ Schzz ‘iax 'K^TX 0 d^ Sp ^ony» ^l^d^tSo ^ tX^ 'à^'C 012^ ^ âd^ni^X 'trltt^xa^^m^TfxyejxX àv'C Szmx^ àigt;tSwlt;l)xt7iK zsm^fiOTfxoïj ^ àxSnibx rrrjyo m^ àMTfo^oKt]/» t^^^tIxov x So^ztI S3dXlt;tgt;X tu. l% âo5uxi ^x'ax iJi7}u àm^t^sn/ g SoyvnH ^ ^^p ^^^^^ '5oidi^iSo t^id

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P P O K A OV

DE HORIZONTE.

Horizon uero circulus eft,qui confpeélani mundi parte ab l'nconfpeÂa dirimit Itac^ in duas partes uniucrfam fphæram fccat, ut alte r um h emi fphærium fupra terram, alterum fub terrarelinquat. Eftuero horizon duplex, alter qui fenfu ufurpat, alter qui folaratione percip^ tur.Ergo fenfibilis horizon eft, qui à noftro ui fu in termino uifionis circûfcribit.Hicadeo no amplius duum milium ftadiorum dimenêtern habet. Qui autem ratione percipitur, ad fixarU ftellarum fphacram perünet,mundum^ totuni in duo lecat. Nec uero per omnem tradhim ur^ bemueidê horizon eft, fed fenfu idem quadrin genu's ferè ftadqs manet.Quo fit,ut dierum ion gitudo 86 clima, amp;nbsp;appareil hg omnes eædê fibi conftent, Audo uero ftadiorum numero, pro habitationis diucrfitate,horizon,clima, omnes denii^apparenuæmutantur. Couenit tarnen, ut habitationis ultra quadringen ta ftadia mu# tationem adauftruboreamue accipiamus. Si«« quidemqui eundem æquidiftantem incolunt, in quamlibetmagno ftadiorum numero, hori zonta quidê diuerfum habet: clima uero idem, happaren tias omes fimiles. Dierum tarnen exi tus initia^, haudquaquaps quieundem æqui* diftantem habitant, eodem temporis moment to euenient. Verum h exadæ rationisexamini ftareuelimus,pro quolibet pudo,in quauis or^ bis

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bis parte mutati fitus, horizon,clima, amp;nbsp;appa-rentiæ omnes euariant, Horizon uero ea ratio* nein fphærarû defcriptionem non adhibetur, quod reliqui circuli omnes ab ortu ad occafum circûaclo mundounà rapiutur, horizon fuæ: pte natura quietcmamat, eodemfemper ferua« to fitu.Si itacp horizon in fphæras adderet,cir« cumaÆsips, etiam moueri,ôônonnûquamfus pra ucrticcm ehe accideret î id quod certe turn captum omnem fijperat,tumà iphæræ ratios ne abhorrer. Verum no incommode eins ab als ueOjin quo fphærarcuoluitur, intelligi folet,

SCHOLIA.

tlori5;on.) In concerto organa cßarmilla fignisnotata M R S C. Hit adtà.) Duo miliaßadiorumreddunt eelx. M.paffuum in terra, tint numt» ri medietas eßmilia paßiium exxv.per quantum fpatium lt;juißat in planicit terra marisue.prorfus uidet terram marine eontingere ealum. De hoc hori ttfinte fenftbiU dixit Strabo his uerbis:Confequenter ita/p hvic poiticum illud accommodates,hori^^onternquidemdebemusaccipere, c^uod terra uicinum eßoeeano. Ardicumautem quod terra attiguum, qua ft fi^umhabitata panis.maximi ardicum fecundum fer/um, cum prior eius traäatio fuifjet dehori:^onte,qui folapercipiturratione. quiautem.} Dhimusahoca» pite quad circuli circunferibunt ealeßem fpharam folaimaginatione. Ati huncmodum horit^onmundanus ealum medium circuncingit ,non autem uinculo materiali. nbsp;nbsp;t^ec uero. ) Tra^um uocat climaxltma utro eß difz

feris fitusregionum, qualem habet una uiciniorem remotioremie altera ab •equatore uerfus alterutrum mundi polum. SMdi4 uero cccc. reddunt xlviij. M. pafjuu, per quantufpatium ubi locus borealior dißat abaußraliori.fiue is ab illofphara recipit abu fitü, cuius fit exempli :Koma palus B leuaturfu pra S horiiipntispunfltsxlii.QuiergolocummutetdißantemMma uerfus boreamßadijs cccc.leuabit B polum amplius unofer'e pundo.Sedqui locum mutettätofpatioaußralioreRoma,idedeponetfphardin B polo piflo uno fere minus partibusxbj.propterea ut ccelitus apparentiirerum effeüus,uno refpondeant pariser in terra atqi cala ad mutitu canonem, Coutnit.) sw dyi

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P P o K A or.


dtjsenim O.fecundiirdtionemPtolemaiJlue D CC.fecundumueterufupt fu:agt;ioncm conueniat mutarefitum fpharipergradiim unum. Sh^utdé.) hocd cjU£ fitum habent differentem interfeptentriortem O' mtridieimutferi Carthago o-Roma,hteebabenthori^ontem uariatumfecundumfigna M S. Spbara enimmB fignojit hoe loco quam altera altior, Roma quidem partit bus xlij. Carthagmixxxij.Locaautemqucefitum habentaquabterdiflantent ab aquatore uerum differentem,quia alter altera eß orientaltortut Conßam tinopolistpfaîf Roma,hate habenthortt^outem mutatumfecudumfigna R C, uideliceteßoRomaßtafub V uertice, dus horizon eßper ßgna M R S C. Porri CÖßantinopolis eß orientalior Roma partibus tequatarisfere xx. Toth dem itafpartibus quarts V R.reuocatafuper R ßgnumhort^ontis.eßuet tex Conßantinopolis orientabor V uertice Romano. Et quia per conßrudiot nem organ: horizon ei' fuut ipßus uertex dißant toto quadrate tigitur O'hot ritqpn ebßantinopobs, dtßabitdßto uertice perquadrätem, numeretur quOt drans ex loco uerticis, Conßantinopolis defignato fuper quarta V R, dtßabit horii^nnConßantinopolis exRcr Cutrinlt;p,quantumipffuertices,ßnieturlt;f apud Rfubhori^onte.Rpud C autem fuprahori^ontem.perhosßnes^li (S' S ßgna,intelbgatur duci perpetuus circulus.U erit horitzon Conßantinot pobsreprafentatusmanentibusRomte,ßtbhoc ßtu fpheeraeueniuntutrotf loco fimtbter apparentia caleßes,quälet nuncplunmas deaquidißantibut crcoluris.cf dierum prolixitate diximus. Sed hoc differunt, quia Conßantit nopoli initia dierum praueniunt Romana, (O' illic uefper prauenit hunc ROt tnanumfecundumrationemdißantiie horit^ontis huiusabillo quaeßhora unius aquinociialis er tertia partis. Q_uod tale eß ubi Roma numerat horant unam er partem tertiam,ab ortu Conßantinopolis numerat horas duas cuM tertia parte ab ortu : er Roma quando meridies, Conßantinopob eßhora fut pra meridiem prima cum tertia unius : er Roma quando occafus Conßantit nopob hora una cum tertia nodis. Sed eßo obferudtio Conßantinopob, fuet rittunccommutato loco fitus einsßib V uertice,er horizon M R S C.Rxillo loco concipimus habitudinem horis^ontis Romani hoc modo. Differentia Ion gitudtnis utriußp eß noßra, gradus xx quibus eß Roma occidetaUonergofu perquarta V C,totidemgradusaffumunturex VfillicßtusinteUigituruert tex Romanus. Ab hoc loco accipiatur utrinf; quarta circuli,ßniet una ab hat rasante apud C, altera totidemgradibusfuprahorirontemapiid R,pereos fines er punda M S intelligatur duci circulus .Iseß horizon Romanus cob latione eius Conßantinopobs. Sunt'f hie rurfusfubduobus locis unius latittt dmis omnid ealitus apparentia fimilia,praterprauentiones er confequutiot nesortuser occafus fic, utexemplopriore expofuimus.ltaRroclustaeitono mine longitudinum, edrum trafldtrationem, quam nosproUxius enarrauit mut,tu nuncearum cognitiopararetur, er poßea in geographicis longe fiet rent manifeßioTa,qua tanto ante meditatafuiffent. Veri ß.') Dixit Pro«

tlM

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c!«t dntfd mutdrifttum [fhane m dijiantta jladiorum cccc.loc ad naflm* rtmrationemadducit, quie fotefific coUigi. CrdJui«nuimrriJidni, diuiili intf liigitwr m minutidi primai lx. Porri lx M. paffuu m ttrra,rtfpÓdtnt gra dui Kill fakpi. seewndKm baue affumptionem, tjlo locus horealior primo mille pdfjifc.lcuatimu! fpharam fuh hoe loco in B polo minuto «no ampliut mtridiani afuu priori. Ejlorurfus locus fecudus orientalior primo nulle paf, (Ausfiatuemus uertieem loei orientalioris froeul uno minuto,ab V utrtict loei priim uerjus R fignum, bof^ fee^uatur fuus illi«ï bori:;on fccKncluiM fxpo/itam pa«lo anterationem. Modern exemplo maiorib. interuaHis afjums ptii, aptdbjmui/pb^ram banc ad calejlii babitudinem.

PteiTÏp laerHu^^tuSiy LvkKui/»

IMlt;rH!/.S^tvos tri ^ KVxA©-, ó ijj^ rZy Ttf Koerfüs TscÄia^iy Xgu 'T^i i^ KO^fjepiuj at)(iéts y^xepi^®' kvk^s -1'^'’ ov ^ó (iSijfOi o u\ias TK )ii(fi: t «gtgóèp, 0 tcc (i^f^ t wKTÛnt tsaiH quot;^^ Cinni /^ ’dhp ó àvxAsç iKivKlt;9S lt;^ Is^ (lóo-iJiu^ ty t^ td/Tiùù TK^iy t/hx^vAxKaiy oji oA« 7« ttSI Manv Ts^t^oepH. » LxtXy^Kepi.'TtU t/i ouros o XVXXsS ^ TCÜï KXTXSM^t^Of/ZieUS aepxt^xjLÇ^ ef^ 'n tt^ xKtvH^t w, ic^ iJ^9lt;f^^ixij'i7iilt;/li](^^xe. It't'rii'^ujo-t^.,x7i^x 7rÊs pSj) 'rliu cu-^Haiy lt;^lt;/loi)u^sxa'iovs •TfiXKoa-'iiss o xir^i (na-HteS^ivis e/lixitkil. Très ^ quot;rfut lt;^ ^^ AÓ^amp;i xgt;içJ.Cixo, xfix ^gP tIui nrx^iOxit ylv^Stxc ’tssx^otAoy-,» 7r^{ tAixiy^ tTi^JiOï ■yivi'nu. (naniJLS^svoi, ^ /\ yXf ttÊs x^ Kamp;^l xgù (tia^iiC^iXii ‘nx^olt;Aoy^ Kew {c^rxfv nv^ilt;gt;i sxt/ltoi v^ ^^X'^*l^^^'^^ ^^ t*^°'’*!^^^*''^S» ^ ‘^ '’^ à7r ewx'amp;Küt Tr^s /van/ quot;ixx^o/lop, e/ltxepo^xt inaviJtC^tt/Sn/,

DE MERIDIANIS CIRCVLIS.

MEridianus drculus eft,qui per mundi po los 2lt; pundum, quod nobis fupra uerri« cem eminct,ducitur dn quê cum fol incidit,mes dios dies,mediascpnodes efficit. Hic etia circus lusjmmótus in mundo eft, uno eodemep in to* ta mundi uertigineferuato pofitu. Necin fphæ iris,qui aftris infigniumr afcribitur,quod amp;nbsp;im

g motus

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motus fit, 56 nullam mutation em reapiat. Sed (quod fenfu ufurpari poffit) trecêtis fcrè ftadijs idem meridianus manet. Rationis tarnen feru^ pulofioreindagineadquemuisgreflumgt;quior tuinuerfusoccafumue dirigit, nouus meridian nus notatur. Adauftnienim boreamue quan^ tumuis progrediare, etiam fi decern millium fta dioruminteruallüinterfit, idem meridianus fet uatur, cum ab ortu ad occafum itur, mutatur.

SCHOLIA.

Scmickadusmefidianitß notatus fignis M V S, necinfphitrhafcrili tur inter reliquos circulas, atjUdtorem, paraUelos, eclipticam, coluros.fd txtrinfecusadtjciturinßarhorisiotis. Sedquod. )^xfuperiorihypotheß fiadia ccc.dant xxxvi. M.pdßuit.^ualiumßadial).dantgradumunu:fiue fiadia ccc.dant xxv.M.paßu:t,ijualium dcc. dantgradum circunferentief maximit, per t^uantufpatiü in terra, ubi dißdt duo loca inter orient em O’ oc cidenté,intelligitur mutari meridianus mcmorahili diuerfitate.Keliqua dut loei ßrupulofioris indaginis,reÿcimus adfuperioré expheatione de hori^óte

P%ex yxÂXKTiKÿ ^CkKsv.

A0fosZi 1^ KVK^s., tf^ôiÿyx^xKf©'gt; ÿ-nsfjJiju vv fxaf ^ui TrAxiet TtiAofcoTra to TjaoTrmi Kt/K^ta, xuviSÿKi e/è t« ^ptC}(y,uilt;sJ.xs witfiÂsi/ovtiKçyj. isiy 7/ to kox/x/ü yivos diu^n ^J. ^^Sl^tstu 3 CUiTtS) -^ TSAX^Si *^* ^ (^ '^‘gt;'(^ t^^^ft Tfici IVT-dfsi! l^y., KXTX tßi 7iUX SitfÓ’Td^amp;'. t/lt 112 00.71X^11^ TWi -:^a7XlS XCpOU^XH OvJè KX7Xy^X^^ Ó 71^1 yxPtXKTi; KVK^S!) tst A Ö av7os 7i)y y^yisc^y KvKÄmy.inyisot yo^ t^ xe^xü^euf AiyovT^ xvK^t, 0/ ?o xii'^ Kit^au tysurdlx 7n xtftxz^x. ^a-i i/é ytiytsot KUK^t l'sifixJxMfi.st^tyoSy^eaJ'iXKistKSU.ó c/jgt yiixaiy ^ ^ai/tcoy. o Jl^’ TÜyxffÓAaiy^ « kx^' iKXsbu oiKKXty óze^y^o i“' (rHye§iifès,lt;)'riSiylt;x^xx7amp;,

DE LACTEO CIRCVLO. OBIiquus etiam eii amp;nbsp;ladens circulus. Hw^ itacpfupratropicos obliquatus ccrni£ Co-flat

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flat aut ex tenui nebulofafubflanria,unus certê cœleftium drculorû confpicuus,nec certa latitu dinedefînitus, fedaliquafui partelatiore,aliqua anguftiore. Quo minus equidemin plerafque fphæras afcribi folctEftautunus è numéro ma ximorumcirculorû: quippecum maximi circu li in fphæris dicantur, quibus idem centrum eu fphæraefl. Suntporro maximi circuli feptem, Æ.quator,Signifer,qui per media figna ducitur, qui per polos ducitur, cuiufqß habitationis ho« rizon, Meridian us, LaCteus,

SCHOLIA,

Vi4 htâta ptr quas cali partes ducatur, traditur hbw ytÿ. magna corn pofitionisPtolemai :quem locû neip totu defcrihimus,netp relinqiàmus omni no. Oelmtabimus aat per dus fumma uefiigiaAnitiumefio apud Centauru, unde peruenit uno margine ad dorfum lupi, altero adignem ara, hinc proi eedit adfpondilespoßremasfcorpionis margineboreai,fedaußrali adpes dem prioremdeurumfagutartj, inde alt;juis laterib. peruenit ad uulturem volantem, inde adgalltnam .• hinc margo feptentrionahs tendit ad caput Ce phei, unde fpargnur in ramos, uno inter orientem er feptentrionem, altero admeridiemerorientem. Hactzonacomprehendit Cafftopeam.latusfepten trionalegenuHertubs:Meridionale,flellamillius lucidam. Kinclatusbo» .reale temlit ad brachiu agitatoris: Außrale ad talum ftnißrum eiufdem,un: deproceditadpedesgeminoru. Margouerooccidentalis, comprehenditma num Orionis, praterit duos canes, procedit ad nauim prope clypeum, inde ad initium redit. Eum ijui uolet defignare,is perfuperfciemfphara cjuaßel la locätur,per quas ducitur inducet colorem candidiorem, reliquosficutin talo uia laäea eß luce perfufior calo rehe^uo.

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H 7MS crv(i7mirt/Si7rtgt;J)Mrlt;lx lt;refgt;ou^olt;iJ'Hi ^K^^oyQr^e/liou. ^^70lt;t ^s t^vies TTS^'n.Mp tfvo p^ OU. TP^t «fw TSrÓKvSyTffO^pit 7007» ’j KépiljUOU ^ 719 MÄtV •^ÓtfiS.,KX7i^yyiMoU Atyo^j t^ Komv^t t^ ygt; 4vX’ï ödf/.K^flót^öj'Ti’ 5 vero t o^KnKip g i 71^2

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vr^f ww 'arÓKss. dt t/è reraip tj«?, a-v^it^ir^us {JtSi' KaftSiicit TT^J tIÙj TtH «hts TffK^aJ^ai/^lii'K^CtT^t Ktthivi^, KiftOpt^V'rOCl dl' cdiTtXl ^^^ -r ^ 7^ KCtrfltü «^KTtKWp ^^ygt;a7^^KillJ KVXAul/y l^iTccfv xa^iAjifOU, c(ljTÓigt;igt;.» d^ 2^t7ioi^(^iir!i ^ 7r^oa§H(jJijilt;i)p xi flSiilf dl. iTT Mt/u/ T^ 779 HÄtV •Srd^odoi/y dlXXiXKVljAvV XX' Ä^TlXl. dt}(lgt;'^l^^'rKl d^ MjTH quot;K^srè 'T^I'^TXyH tXXfjtl^tVV XV' xKv.) éff xsnxi xniro t ^ 7^ xoa-(ji.efi txxfzi^t^ài) KVKAcy.TÜiJ j W^XXTCDil dvo ^IfSipy H •Ósrè 7^ ^n XX^ »{^£i OtKU^X XX Toix«^ crv^iC'z.ëxxii/y uÿl (jXi' ^ /xfixci ovGi: ais t'^isx quot;^1 di KX (.tvfiddx; sxdtaip-, a^d^do ttAxamp;s ^t iy^isx do H^urv,

DE Q,VINQ.VE ZONIS.

TOtius tcrræfupcrficics fphæricaeft,8ô diui diturm zonas quinep. Ex quib. duæfunt, quæ circa polos dcfcribuntur, frigidædidæ, pp maxime abfu n t à folis orbita : erdem ob frigo# ris iniuriam paria habitatæ.Determinanturau# të polos tier fus ardticis circuits. Quæ uero poft has deinceps habent,quôdmcdiocriteradpræ# tercuntem folem fuut fitgjtemperatæ appellant, habent^ in coclo limites arcticos, tropicos^ cir culos,quibus interiacét. Reliqua,quætnter me# moratas quatuormediurn loeft tenet,quod fub ipfo folis tranfitu iacet, torrida nuncupatur, à terreftri fquatorein duas partes diuifa: is porro fub mundi æquatore porrigitur. Sed ex tempe# ratis altera à nodriorbishominibus incolitur, ipfa longa propécentum milibus ftadiorum,la taferèdimidio.

SCHOLIA.

Tof ittf terra, calum non minus cjucim terra diuiditur in tjuimjut ;çofllt;« relut luat. ex hit dua funt, uideHeet i^ug ex polis Ai, ey bis uierna fignU

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s o AI P A.!

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Ti^as •? T- PgoxAif xifiù^xs.

DE SIGNIS COELESTIBVS.

Cigna ftellis infignitadiuidunt in partes très, 0 (^ædarn in fignifero locatafunt, quædam feptentrionaliauocantur,qugdâauftrina.Qug itaq^in figniferofita funt,duodecim animalia funt, quorum nomenclaturas alibi diximus. In qs duodecim fteUæ quidam funt,quæob quaG dam quas referunt notas, proprias appellation nés mcruerunt. Siquidem fex n umero, quæ in tauri dorfo uifunt,Pleiadas nominâtur.Qiun« queuero, quæincapite tauri cernuntur, Hyan des dicuntur. Stellauero, quæ pedes gemino« rum præcedit. Propus quafi præpes uoeatur. Qtiæ uero in Cancro nubcculam referût,Præfe pe uoeant. At duæ quæiuxuPræfepe collocatg

« funt, Afelli dicuntur. Prænitens autan fidus, quod in corde leonis notatur, fimili cum loco nomineleonis cor dicitur:ànonnullis regia ftel la,quod qui fub ea nafeuntur, regiam natiuitan tem fintnadi.Sed quæ in uirginis fumma,fmin ftra manu hæret,fulgida fané fteUa, fpicâ nomin nant.StcUulauero quæ iuxta uirginis dextram alâ figitur, Protry getes dicit. At quatuor fteUg, quæ in fumma aquari] dextr a uifun t,V r næ n 0 menhabet, Qtiæ uero à pifeiû caudæ partibus u '- nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;fitæ

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ft PPOKAOY

fitr deinceps funt,græcelini, latine Iincæî uti ut quibufdam placet, If neolænuncupanmr. Sunt fuq^in auftrfnalmeaftellæ nouem,fn feptemo* naïf qufnqj.Sedprgfulgês fydus, quodin fum« malfneacôfpfcftur,græcèfyndefinos,latinénos dus nuncupatur.Septentrionalfa funpqupeun queadfeptentrionêfîgnfferi fitum habent. Sut autem hæc: Vrfà maior, urfâminor, draco qui inter urfas locat. Ard:ophylax, Corona,EngO5 nafin,Serpentarius,Serpens,Lyra,Auis,Sagits ta, Aqufla,Delphinus, Protome hfppf, hoc eft, prior equi portio,fuxta H fpparchu equus, Ce« pheus,Cafiopeia, Andromeda, Perfeus, Auris ga,DeItoton.Etqufpofteaà CaUfmachoin as ftrarelatus eft, Berenices crinis. In rjs rurius ftel ly qugdam,ob notas quafdam intégras,quas in iècontinent proprias appellationes funt forti« tac. Nam infignefydus, quodfupramedia Ar« élophylacis cruraiacet, Ardurus appellat, da« raautem ftella, quæiuxta Lyram pofitaeft, to« tius figni nomine Lyra dicit.Quæuero in Per« fei fumma finiftra fpedtatur, Gorgo nee nomen habent. Sedquæin fumma eius dextra notan« tiir, ftdlulæcerte crebræ paruæ^, falcon confi« ciunt.AtilluftrcIydus, quodin aurigaefiniftro humerocernimus, Capra nominamus. Duas uero exiguasftellas,quæin fumma eiufdem au risæmanu fipuntur, Hoedosdicimus. Auftri« na fignafunt, quaccuepad meridionalem Ggni«

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X lt;gt;nbsp;AÎ P /♦ nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;r?

ferî partem funtponta.Eorû nomma hæcfunt: Orion, Procyon,Lepus, Argo,Hydra, Crate* ra,Coruus, Cen tau rus. Fera quam Ceraurus te net,Thyrfolochus quécentaurus prcfcrr,Thu ribulum, Auftrinus pifci’s,Cetus.Âqua quy ab aquario funditur.Flumen quodab Orionede* fluit. Au ftralis coron a, quam nonnulliurani* fcumuocauere, aefià cœlo diminuriuum deck'* nes:ôCiuxtaHipparchûcaduceus. Inps quoep ftellæquædam propriafibi nomina uendicaue reiquippelucida (tella, quæin Procyonecerni* tur,Procyonappellatur.Quæuero in orecanis confpicuo fplendoreafpicitur,quod(ç yftus in* crcmentafecû affèrreputatur, canis eodem quo totumfîgnû, nominecenlètur. At fidus quod in fummo Argus gubernaculo fuîget, Cano* pus nominatur. Hic in Rhodoægrèconfpici* tur, autccrtèabgdirislocis. In Alexandria uerb prorfusnon cernitur,utpote uix quarta figni portione,fupra horizontem extante.

SCHOLIA.

Sunt düd pffuüdrid nomma ßtUarum d Pro do non commemorata. tjine PldaiitsCritfr,Latine fuceuladicuntur,fine fidusparibaum, quiGraci Pretry^^etes.La'ine Prourndemia,uel Anteuindemiatortabergemmorum tippeUaturTripus. Duaclarté inantmoribuscornibuscancri, O'iresobs feune uocaniur twbilum. Juxta caudam leonis obfeurte yij. dida Berenicet cnnes. qtia:inptfloreleoniscordicitur, eademamp;Tvberone. QUee inc4a fite canis, ifis uocatur: tjUte utro in ore, syrius, teilte 13quot; Canicula,Canoput ttiamuocotur, Ptolemton, signaporrocaleßia, 13eorumfingubcßdhi b fie

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P P O K A OV

ficmfplxtraminfcrihuntur, tabula cß uocataradicum ßcllarum: er quant nos aiio opere in hune ußimreduximus ex radieibus Ptolemiti.ada:tatcm no ßraannu chrißmati M. D.XXHiI.In ilia in lineauoeabuh ßella affumpta, fenbitur numerusßtb tuulo, AfeenftoreHa: itemalius numeruscregioßib titulodeclinatio. Aßenßo refiaeßeireulusmaximusdeßgnatusper polos mundt A B, cquashhet feflionesiequatoris.eutus generisßint hl quos co luros itocat Proclus: inttiumearum aßenßonum incipit inߣi.one uema, er fucceditfuper aquatorem,ita ut numerus indicat. Ergo aß:enfiür(£la,eßt dißantiacentrtßellainßtperßcie caliamedietatc totacolurt A C B. De: clinatio,eß dißantiaßella ab aquatore ueißts außru ucl boream fuper qua: bbet afcenfione. Ea acciptttir in circuits, quos uocat Proclus aquidißantes fubcapite, curquinepduntaxat aquidißantes, Hltcinqutens: (itiintsr ßella uniuerfain aqutdißantibus circuitsquotidieferuntur. Burßisßquidemße: ri nequit, ut uel aßra probe in fphara locentur fine omnibus aqiitdßantib. circuits. Deßgnantur atitem, ut illic quoque annotat um eß, ex utrotp polo ÄB,i2-extenfioneperquaslibetfeclionescoluri A B É P. Ems generisßtnt quiperftgna K c? H, c? G cy L duflißtnt.fefliocÜmunisduorucirculori (nempe afeenftonis re fia er dechnationis) dicitur radix centri ßella. Igitur aßumaturßellaquapiam, utpote fpicauirgmis. Afeenftoeiusreflaprafert numerumgradus c xciUj. erß:mis,alßmaturßiperfphara punflumaquO: toris totidempartib. dißansex coluro A C B.lspunfiusßatuaturfubar: millam A AE B. Declinatioporrbillicin tabula feribitur A,X,ideß, au ßralisab aquatoregradus x. Ergonumerenturex AE fignouerfus M toti dem partes, in communißflione fphara crarmtlla A AE B,ßgneturpun: flus fuper fphara. Eaeßpofitio fpica uirgmis refpondens cognatoloco in fuperßciecah. Locaquoquein terramfertbuntureademrationequaßella. Sed fupputatio fuper aquatoreuadtt contrario modo, er ßatuitur initium apud D feflionem,fupertftoto femicirculo A D B ,quiperinfulas fortU: natasduciturtinde'ipcrefcuntnumeriuerfusfcmicirculum A CB, qui per finus ingradtbus clxxx.indeq; ad initium redit. Deinde quaillic afcenftones refia, hic lógitudinesterquaillic deelmationes,hic latitudmes cenfentur. Eiuseßoexemplumurbs Borna. Eongitudo ex A D B gradus xxxvi. cum tluabustertys,latttudo xlij.fere. Badicesetiamßellarumpraterea figunt tur fecundumpofitionem adecliptieam, quaradices prope folaobferuans tur. I« tabulaßellarum in linea uocabulißella, feribitur numerusfub titu lo, longitudo: item aliusfub titulo, Latitudo. Eßp longitudo dreulus mit ximusdefignatusperpolos K L eclptica,erhuiusquaslibetfefliones,cu: iusgenerisfunt vi. defcripti in fphara defignantes xÿ. initia fignorumrP dbad. Initium longitudmum ineipit !i feflione uernaapud C,erfuccedit mt merut

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intrusfecundumfi^orum^odiaàordinem, Ariet,Taurus,o-reUijUit. Eri go longitude jlellacß dus diflantiam fuperficietotacaliextotamedietai te K CL, Latitudo fielLeeß dus diftantia ab ecliptica uerßes außrumuel horeain. sunt autem hi ijuoque tequidißdtes ftbiamp; ecliptica deßgnati ex po ht K o-L tanquameentris.crqualibet fedione circuit longitudinis K G L. EiHfgenerifßtnt aquidißantes xtj. ipfi ecliptica, qui umnque ßniunt la titudinem i^odiaci. Horumcirculorum, nempe longitudinis cr latitudinis, communis fedio eßradixßella. igiturßifpendaturfpharam polis K er L: fiueQubi id efl minus commodum') polus L ecliptica ßatuatur fubv ßgnum uerticis, itauttota ecliptica incedat per totum fitum horix.ontis, cancerlp apud m,Capricornusapud s fediones hori^ontisermeridiani,Libralt;pa3 pud R, c Artes apud C communes fediones horizontis amp;nbsp;aquatoris, er tebpticaßatuantur. sicconformata er confrmata fphara,infcribantur quotlibetßella,quarum latitudoeß borealis. Bßo exempli caufa Ardurus, longitudeeßLibragradusxvii] .mtnutiaprima v. Hacparsfigniaßumaa turfuper fphara,illucadmoueaturquarta V R cum dus latere eunteper centrum V uerticis. LatitudoportolUicin tabulafcribitur B xxii.c fet mis,ideßborealis, totidempartium. Ergonumerentur fupraquarta R V, tx R totidem partes, er in communi fedione quanta er fpbara figatur pun dum illußre. Haceß radix centri Arditti. Pro ßeltis, quarum eß lat tudo außralis,commutänduseßfitusfphara,ftcut polus K fißatur fub V uert ticem,fuerit tune Capricornus apud M, Cancerapud S fediones, Libra a^ pud R, Ariesapud C utpridem,reliquaqutfuperius. Biuseßoexemplum fpicauirgmis: quam rurfus affumimus, ut demus darum experimentum, quemadmodumutraipraibx eandepofitionemm fpharafadtßella. Longi tudoeßLibra xrq. cumunaquintapartis. Latitudo A,ideß,außralisduo, hinumerenturfuperquarta R Vex R. Quartaueroadmoueaturfuperpar tem longttudinis in Libra,tuncin communifedionequarta erfpharafga turpundum,radixcentrifpicauirgmis. HicinRhodio.') Rhoduslatis tudinemhabetgradus trtgintaerfex. RadixCanopi, qua propiorfitatati Prodi, Afeenftoreda Ixx.femis. Declinatio xlix.femis: fecundum hanc radicemponaturßellain fphar am, conforme turea fecundum ft um Alei xandria,merfusuidebiturpolus A fub ßgnum M horizontis, quotpartii bus B polus leuatur fupra 3, nempe xxxi. Defignetur igitur fecundum hat partes Ant ardicus A H,maxtmusbmesillicAlexandriafiderumfemi per occultorum: fed is eß breuior pundis nouendecim, eo aquidißantedu» do perradicem Canopi. Brgo ßella longe eminet fupra horizontem Akt xandria gradibus nouem, ßatuatur fphara ad rationem climatis Rhoiüt tnfis, Antardicus A M comperitur breuior,aquidißante dudoper Rhot h * dumgradk

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«• F P o* K A OY S « Al P A*

nhodum gradtius quinijut mertdiani ftrè. At is eft breuior pun flit tfnatiut Cf femis, eo ctquïd.liante duflo per radieem Canopi : ergo leuaturfielU dlic ^hodigrathb.(quatuor arfemis. 'Exhacoflenfionecoumcitur error loet prtt fentis: nonenim pror/us non ff mi poffrit Alexandrite, lt;jui Khodi cernitur, quinillic magis cemetur,quanto er maior eßjielliealtitudo.ciuartaautem pars fignijuntgradusfeptem er femis. na:c lefho ftcut eß altena à poteßos tefphterte, fic ifud fuerit altenilfmum, ut lapfum tam manifeßum trihuai mus autori. Nos adteflum diemus a le flore quopiam par um eau to, liquide er in reliquis partibus eins capitis, nihilßel larum attigit ampliusfupra nomenclaturam.

Potuit ergo eodem exemplo hu etU finite fermonemita. Atfydut quod in fummo Argus gubernaculoful

^et, Canopus nominalur.

*'*N1S SPHAIRAB PROCLJ.

PARS

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PARS ALTERA DE CANONICA PER SPHAERAM OPERATIONE.

Avenus fcquuti Produ/edmus nu dam indicatura circulorum fphgrg, quibus cœlitus apparétes res tranfis guntunSccundum id,apcricmus fe« que tdcrmonc can onicam Operationen!, mo tus ccdeftis imitabilem nobis hoc exemplari orgas no. Totarn autem operationem, ad pauca atep hæc neceflariacapita adducemus. Ad hoc uero negotium prædpuepoftulantur, quæin indus dione diximus, ut machina datuatur in planis ciem correda quaquauerfum ad pquilibrij exas mcn,ut^meridianus M v s ftetfuperficie mes ridiani ccdeftis : fiuequod tan tun dem eft,in lis ncacardinis fecudum magnetis regulam.Vtue roarcus s B,adcertumutillicnumerüaftumas tur, interim nó requirimus, fed alterum hoc, ut gradusfolis certus fitaddiem,fub quo fit opes ratio. Is autem fic propè ad uerum condpitur, fol ingrediturinitia fignorum circitcr idus men fium,utarietcmcirciter idus Martias,taurum circitcr idus Apriles,folftitiu circitcridus Iulias, Sic^ figna reliqua circitcr rdiquas idus, has ras tionegradus,fingulicclipticæab initrjs fcquens tcs,tribuürur fingulis diebus fcquentibus idus, 6ó obueniet gradus folis,quo cum erit ad dient opcrandum.Qiiod fi idem exacte queritur,tras dicuseft canon in opereSapheg, undepetatur.

h , CANON

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« nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;C À N o N I C A S P B AB R AB.

CANONPRIMVS.

DE CIRCVLO ALTITVDINIS ÉT , nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;uerticalifoliî.

/^ Irculus aldtudînfs defignatur circino ex v polo horizons utccao^Ôv extenfione qua# IibetperquempiamuerricaliuniVMjUel v R,uel v c, uel v s : fun t^ in rircuK ex genere æquidi# ftanrium horizonn numéro xc. inftar æqiudi# ftantium æquatori, per eos captatur eleuario fî# derum fupra horizontem. Verticales funt por# rionescirculorumin fphæramaximorum, ue# mentes ex uerrice 00 eodem polo horizonns, fu perdus quaslibet partes,fun t^m fuo generead horizontem quodafcenfiones redhead acqua# torem,amp;longitudines adeclipncam, per eos ca ptaturdiftâtia fiderisexmeridi'ano v m, fine V S,quartacv r amp;nbsp;v c tenent nice,06 faciuntoffi dum. Pro uerticali condpiedo, index ftatua# tur fuper quartam uerticalem,refpidêtem ad re# gionem fideris inpartecoeli.Qtiartaautêmo# ueatur contra fidus,i'ta ut umbra ex apice mdi# cis ingrediatur per mediam fpinam quartae. Ar cus horizons interquartam flatus meridiani uicinius notatnumerumuerricalis, ideft,quan titatê diftanriæ fideris à meridian o. Efto excm# plicaufa quarta v R per quafitoperario, arcus R s notât diftannam ex imo coeli,arcus R Mdi# ftanriä ex medio cœli.Pro alritudine concipiert da,manête quarta in fitu prüfen ti,moueatur in# dex

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o P B R A T 1 Ó. nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;lt;,

tlex proplus logiusuc ab alterutro pucto v, uèl R ad alloua parte,ubi index confiftens,dus um bra in pedê côtrahatur Sc tota abfumatur. Tûc pes indicis inter diuifiones quartæfuper fupres inafpina,indicataltitudinêex horizote. Arcus uero quartæ à pede ad V fîgnu,indicat diftantià fideris à uertice. Latera quinenâ indicis defeens dentia per fuperficiem quartæ, indicant inter di menfiones laterum eafdem, cum altitudinem fu prahorizontem,tuni diftannam à uertice,

CANON I I,

DB LATITVDINE LOCl CONClPlENDA rx dlticudinr fiderit t? uerticdli ddtit.

T Euabiturfignù B fphæræex s horizontis, hadenus quod gradus folis in ecliptica no« tatus,ad diem admotus fub uerticalê,incidat pa riter in deprehenfam altitudinê.Hoc fitu arcus V Eeftquefitalatitudoloci,ideft, diftantiaeius uerfus boream ex perpêdiculo æquatoris, amp;: ar eus s B altitudo poli, parubiep latitudini con« ceptæ.Ergo alterutro arcuexplorato,alter eft exploratus.

CANON 111.

DE GRADV SOLIS CONCIPIENDO AD lid dirmexaltitudine^ uertteaU, exqiie loei huitudinedatii.

GRadum folis pridem concepimus ex ratio ne extrinlecus petita,uerü hic eu dem cons cipimus ex ipfa poteftate fphgræ. Altitudine amp;nbsp;uerticaliconccptis,5carcus B affumptofecuns dum

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o .CANONICA PEMSFR AB RAM.

dumlod Iaritudinem,moucatur fphæraabor* tuin occafum, donee gradus quifpia edipricae ueniat fub datam (èdionemaltitudinis 06 uerd call's, qui incident,eftillic quefitusgradus folis ad diem. In eodem gradu uoluatur fphæra fub meridians A ae B.Ärcusmeridianiintercon^ ceptum gradum amp;nbsp;AE fignum mcdius,clt decli nario præfens folis ab æquatore. Den iep arcus meridianiinter MÜgnurn horizontis 06 gradu prüfen tan, eftakitudo folis meridianafub di^ em conceptum.

CANON 1111.

DE LINBA CARDINIS M S, CONSTU tMfnc/4 inplanicic,txaltitudinefolit meridtana, TRanfponaturindexfupcrarmillamm vin altitudinê meridianam explora tam,amp; tan poreuicino medi] diei continue obferuetur,amp;^ dirigaturinftrumentu haótenus quod tanpus ueniat, quo umbra afTumatur in pede in dicis, nufquam declinans amediafpina.Hoc fitu OP gani pedes eius qui defcenduntin planidem eX s fignis,ftantinlineacardinis, fiuefuperfi ciemeridianimudanfnotetur is finis fignis,S^ per hæeducatur lineaperplaniciein, ad pcipc^ tuu ufum Pedes quoep organi qui defcendunt in plan ici c, ex R amp;nbsp;C fignis horizons, fiant co* dem opera in linea decumana, quâta ea longiHî me inter ortum Só occafum extêditur, fignetur ipfa

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o P B R Â T I o. nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;«f

ipfa quoép.Gradus quoCpequatoris,qui fîmul cumgradu foil's ftatfub ineridi'ano,uocat afœn fiorcda,gradus prüfen tis de ecliptica, Ô^infigni ter notetur:nanqjeius ufus eritad fequentes plu rimas obferuationes.Denic^Iineacardinis M s, poteftcouftituiquolibetalio extrameridiê tem pore, Efto exempli caufà tempus iftud matuti« num, gradusæquatoris : ilia dico afeenfio reda gradus ecliptica:, dimoueatur ex meridiano uer fus R horisxjntis, per gradus æquatoris quotli buerit. T une per locum folis in ecliptica educa« tur quarta v a, amp;nbsp;notetur alatudo folis ex horis 2^0nte in hoc fitu, illue ftatuaturindex. Poft di« rigatur quarta v r continue,motu totius inftru menti côtrafolem, donee occaßo incidat,utum bra abfumatur ad pedem indicis, fuaç ipfius Ia titudo complcétatnr utroep fine lantudinê quar tæ,neutro latere ex ca declinans. Vbi hoe dcpre henfumfucrit, armilla M v s, quarefpicit,inde inceditfuperficies meridianimundani, amp;nbsp;linea M s ftat in linea cardinis,notetur eaperfummos pedesorgani, utdieftum eft,

'CANON V.

DB ARCV DIVRNO ET NOCTVRNO fub alJùmftoÿradu foüt.

/^ Onceptus gradus folis, ad diem ftatuatur in alterutram fedionem horizontis, orien talemfiueoccidentalem. Efto ueró exempli eau i fain

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«^ nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;CA NO N l C A SPA AB R AB

fain orientalem, fuperautemæquatorefiatno«' tafub AE fignocómunripfi Sómeridiano. Ab hoc figno æquatoris numerêtur fuperipfo gra* dus ufque ad alcenfionem redam pridem com pertain, is eft arcus femidiumus, is geminetur, 00 prouenit integer arcus diurnæreuolutionis folis fub aflumpto gradu. Is arcus diftribuatur per xv. amp;nbsp;proueniunt horæ amp;nbsp;partes prolixita# tis dieiprælentis. Item arcus diurnusfubtraha^ tur degradib. ccclx. fine numerus horarum di^ urnarum fubtrahatur ab horis xxiirj.refiduum eft quan titas nocturna. Quot graduum fuper æquatore eft arcus, nel is nodturn us, ucl tile dnir nus, totidem etiameft idem arcus fuper parallel lo folis prüfen ti.Igiturarcus gquatoris diurnus, numerat portionem parallcli diurna,amp; noCtur nus diurna. Hæccp eft uniucrfalis ratio,qua co« gnofcitur omnis paraUeli portio fupra horizon tern leuata, 00 portio reliqua fub code deprefta. Et qua plane enarratur, SCponitur in exemplu caput Prodi, de occultationib. amp;nbsp;emerfu fideru»

CANON VL

DE H0RÄ DIVRNA AD TEMPVS.

HOra eftinteruaUum tempon’s conceptunt lecudum aliquot partes, uel cquatorisud unius illi æquidiftantiû.Eaïnteruallaaflumun tur, uel peræquales arcus fecundu omnes parah Idos

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o P B R A T I 0. nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;«7

lelos, Ut puncta quindena, amp;nbsp;hæ dicuntur hos rææquales, fiuepcrpuncta inæqualia nunc plu raxv. ut in fignis borealib. nunc pauciora xv. ut in fignis auftralib.amp;hæ dicuntur inequales, fine temporales, 06 aflumutur fècundum banc rationc, utomnesparallcli feorfim portionem diurnam partiarnurin partes æquas xf). amp;nbsp;feor fim noéturnam in xq. poftea horæ æquales ua rie numerâtur. Aliquæ incipiunt ex medio die, ÔC definutadimum cœli ad xfj. Hincrurfus ab unoincipiunt, ÔCdefinuntad mediumcœli in xq. hæferèdicunturæquinotfliales. Aliæaboc cafu folis ordiuntur,amp; continuo incremêto fuc cedentes, finiùtfub occafu folis diei fequêtis in numéro xxiiq. Siue ordiuntur ab ortu, amp;nbsp;fini« untfub occafum eius diei in numéro quantita« tis diurnæ. Rurfus fub occafu ordientes,finiût fubfequenrisdiei ortu,innumero quantitatis noôturnæ. H æ horægquales tan turn dicun tur, nonæquinoéfiales.Horaæquinocfrialisficcon cipitur : Concipiatur alritudo amp;nbsp;uerticalis folis ad tempus obferuarionis, fub hune locum ad« moueatur gradus folis, tune porrio æquatoris deprehenfa inter meridian um amp;notam a fern« fionis recTæ, ipfius gradus notât horam. Efto hæc porrio ab ortu ad meridiem, gradus quin« déni ex mendie notant horam xi. trieeni decis mam, quadrageni quini nonam. Ad eum mo« dum diftribuemus horas reliquas, occurretfup i i nota

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«8 nbsp;nbsp;nbsp;nbsp;nbsp;CANONICAB SPHÄBRAB

nota afcenfionis redhr, gradus foil’s dénomma* tio horæ amp;nbsp;partis. Vcrû efto obferuario tempo reà mendie, gradus æquatoris xv. à meridie di cunthoram prima, gradus xxx. horam iecunü dam: atq^adhûemodum diftnbucntes arcum sequatoris, cadet Riper no ta afccfion is reCta^gra dus folis denominatio horæpræfenris.His h os ristotapropè Germaniautitur. Hora ab omi folis fie exploratur. Gradus folis fiatuann hori zontem orientalem, amp;noteturafcenfio reCta fo lis. Ab eagradus xv. danthoram prima ab or# tu,gradus xxx. fecundam,gradus xlv. tertiam. fie continua fucceffione per incrementa hora* rum, ufq? fub occafum. Præterea noteturarcus æquatoris inter R fignum,amp;afeenfionem reCta folis interceptus:Is arcus dicetur à nobis differ rentiaa(cenfionalis,habcatur memoria quot is graduumfit. Hisita compofiris, Ratuatur ut anteagradus folis fub fedtionem alritudinis amp;nbsp;uerticalis, deprehenfam ad conftitutum tem* pus,tune à loco æquatoris,qui diftat ex R figno fecundum numerum diffèrœaæalcenfîonalis, memoratæ numerentur horæ,ufque ad præfen tem fitumaicenfionis redlæ, prouenitep den o* minatiohorætemporisexadîa abortu. Hisho* ris duo Germaniæpopuli utuntur, Norinbur genfis, Sd Ratilpontanus. Horaaboccafu fo* lisnumerata,ficconcipitur. Statuatur gradus in fuperficiem horizontis occidentalis, amp;note tur

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o P B R A T I 0. nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;«9

turafcenfio reda foil's,ab eaincipi'untnumcrari horæpergradus quindecim æquatoris,ordien tes ab una, itautin bis ab ortu diximus. Notes tur arcus æquatoris inter afcenfionem redam foil's,8lt; c lignum horizontis interceptas. Is ars eus ita ut prior, dicitur differentia afcêfionalis, teneatur memoriter quot graduum fît, poftea locato gradu folis in fedionê altitudinis amp;nbsp;uers ticalis,numerenturfuper æquatoreexarcu pari difterentiæ afcenfîonali horæ ordine cotinuo, ufque ad afcêfîonem gradus folis,fuper ea pros uenitdenominatiohorf temporis exadi ab ocs cafu H ora diuma inæqualis fîc accipitur.Semi diurnus arcus folis repérais, per canonê quins turn diuiditurper vi.amp;lproueniuntgradus des biti interuallo horæ unius. T une fada ad terns pus obferuationeper altirudinê 00 uerticalcm, arcus æquatoris inter diffèrentiam alcenfîonas lemortiuam, SCpræfentcmlocû afeenfîonis res dædeprehenfus, digeraturper fadainterualla, amp;nbsp;prouenitdenominario horæinæqualis. His olim Romani, Syri, fcrècp an tiquitasufa fuit. II lis ueroab occafu utunair hodieltali, Boémi, amp;nbsp;Poloni. Hæc fîc exequi per partes opomiit: propterea ut Proelus inteUigaturapudomnes communiter, qualicuncp tandem illipartiaone temporis 8^adnumerationeutantur.

i » CANON

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CANONICA SP H Aß R AB.


CANON VII.

DB ALTITVDINB SOLIS SVPRA HO. r^ontfm conciftenda ex dato loco folit in horit.

AScenfio recta, gradus foil's ftatuat fub me« ridianum v M,inde dimoueatur ucrfiis R fignum horizontis, fecun dû partes refpon den tes interuallo horæunius æquinoôtiahs, ßue i U kus temporalis:hanim nanquemeridianus eft æque médius,fecundu denominarionc amp;ini« dû horæ intégrer. H oc fi tu fpbere firmato,quar tavRadducat fupergradû folis, arcus quartæ inter R fignûeius,fiuefuperficiem horizons 00 gradum folis, deprehefus eftalntudo fi der is ad horaunamcitro ultrôue meridiem quefita. Eo« dem exemple in reliquis fiat In horisab occafu 8^ ortu numeratis, Gradus folis ftatuatur in fn# perficiem horizonris oricntalis, 8f obfeructur gradus æquatoris exiftens in medio ccrli,is gra« dus dimoueatur ex meridianouerfus C fecun« dum partes xv.Sub hoc fitu trâsferatur per gra« dum folis quarta v R,et arcus huius inter friper« ficiem horizonris amp;nbsp;gradum folis deprehen« fus,eft quefi ta alritudo. Cû uero ad tempus fue rit uentum meridianum, amp;nbsp;gradus folis fteterit in medio cœli, gradus æquatoris quieft afeen« fio recta, ft ab it in c figno horizonris. Ergo pro horis reliquis à meridie, dimoueatur eadêafcen fio redra ex C, n er fus imum cocli lecundum gra dus xv. per gradum ucro folis extendatur quar tav C

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- ’ o P E R A T I 0.

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U V C, Marcus hums inter horizontem Sôlôi cum fob's eft al ri tu do. V crû in his horis ab occa fu numeratis, eueniet quod ortus folis non ind det in articulos horg intcgrg,ergo quod reliquu eft, ad fequentis initium captetur fuperæquato re, tantundem^ accipiaturex afcenfione reda uerfus ahorizonas.Etpars æquinodialis qug attingitur, efteadeftinataad operationê, fecun dum initia horarum numeratarum ab occafu»

CANON V I I I.

3quot; DBVMBRAEX ALTlTVDlNB ad horam conßitutmUm.

DVcatur extrinfecus in abaco per median! planiciem tan quam horizontem linea a B,ex qua affumatur porno a c,eftc fîgnumlo« eus Sciotheri eredi in planicie. Ex c educatur perpendicularis c D,uidclicct axis horizonris, ex eo affumaturporno c E proceritas Seiothe* risgt;ex qua ducatur perpendicularis ad c D.gqui diftans aûtipfi c a quæ fit E F, S^ ce mro educat quadranscôringensfigna F D. Is in fphæra, re præfentat quartam quâlibetdefcendentê ex v uerticefupcr planicie, 80 A C B refertquamlibet merientê ex affumpris Riper horizote fignis^du dâ per mediû centra. Quarta diuidat in partes æquas xc. infcriprio fit ex F in D. porrô Sciothe reus c E diuidatin quotlibet partes gquas.ERo uero

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ft nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;CANONiCÄ SPÖ AB R XS

* quot;nbsp;uero exempli caufaxiii'j.fccüdumratios nem affumpta, quod pedes vi.amp;Sfèmis, reddant fuam cuiufcp menfura, amp;nbsp;Scios thereus referat ftaturam hominis obfer^ uantis.Sciothereus C E transferatur eu circini æquilatarioneper tota planiciem E B, Sóhxcinterualla fubdiuidaturper a tredecimas partes c E,inicripno fit ex c uerfus Bîatc^hæceftnoftrædefcriptio« nis formula. Nunc tandem ueniamus ad umbram coUigendam ex altitudine quacunquedata. Affumatur altitudo ad horam datam.Edo hæc exempli eau « nbsp;nbsp;nbsp;nbsp;(à meridiana, capitis arietis graduum xb

virj.in latitudinelocigraduu xlij. hæc altitudo numeretur in quadrante ex F in D. Hineftatuaturrégula,ÔCtranfmit “ taturper E medium umbilicum, note^ mr^fedtio in E b, fithæc G. Eftumbra E G meridianacoceptaex data altitude ne, ficin reliquis operandû eft. Poft hcc

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XVII

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OPÈRATIO. nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;1^

digcrantur tab dig eer ris areolis:à quarum fron tefignentur partes zodiaci’jexlata'eautem des feendente fignentur horæ: 8ó in horum cornus ni angulo notent conceptæ alritudines,amp; um? bræ fecundum formulam fubiedam. Qui uero ida paraturus eft,utex his obferuet,debebit aG fumeregradus denos fignorum, quoru annos tabit alritudines amp;nbsp;umbras per boras fingulas, quo exadius obferuatio refpondeat ad cedefti urn habitudinê. nam ita ut nos per fumma figs norum capita tabulas digeflimus,non poteft al titudo hge, amp;nbsp;umbra exacte fatis per to turn relt quû fignumindicare.Sed nos ex emplît ^ppofti imus,quodefretundeopusabfolutû déformas ret. Quiuelitper memoratas umbras obferuas re,conftituat locum folis in fignis,per ca qug ini tio canonicæoperationis præfati fumus:eriam conftituat genus hore.Efto exempli caufadus ab occafu.Secundû ifta,obferuator ftet redus m ueftigiotet notet finem umbrg ex uertice pers uenien tem ad planitiem:et metiatur à plan ta ue ftigq pedes medios,quifuntadnotam finis um brgtcumhocnumeroingrediaturtabulamfub figno concepto. Numerus horæ è regione,eft ea quæfita. Sed cueniet, quod idem numerus non reperietur fub figno concepto.Hic itaerit ad ^pinquam rationem operandu. Efto exem pli caufaobferuatio fub figno capricomi, V ms bra deprebenfa,cft pedum mediorum x x x V,

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CANONICA SPHABRAB


Is numerus non reperitur fub limite, fed pro* ximemaioreo x x xvjq,amp; minorxxxiij.Itai que Ut v eft medium ad i q amp;nbsp;v q, ita moment turn obferuationis, eft media bora ex x V i rj ad xix.

CANON IX.

DE ALTITVDINB SŸDERIS.AD HO ram, dtif linea cardinis,C2- latitudint loci conßitumda.

HÄc uia uctei'es ufi fuerunt dimatibus in® dicandis,fub mentione habitudinis mu® tuæ gnomonis adumbram.Ergo hunc canc® ncmtralt;ftamus,unde eiusorigo habeatur. De® in Je lectori,fuo ipfius iudicioftet cenfuraqua* tenus probetumbras, quæin operedere rufti^ ca apud Palladium extant. Vmbra deprehenia» transfératur pari numero in puncta planiciei ex c in B,PerhancnotametEcentrum,eficiatrclt;fta in quadrantê F D.Ärcuseius ex F ad lincam, eft altitudo refpondens datg umbre.Efto exempli caufaobferuatio hæc temporematutino.Igitur reliquum operis,agcmus per quartam v R iph^ ræ nofti'æ.In ea ftatuatur index fuper parem ab titudinem ex R, amp;nbsp;continue obferuet tempus, amp;nbsp;quarta v r contrafydus admoueatur: quod tandem index cius abfumat umbram in femet, denied lateribus timbre,comprehendatarmilb craftïtudinê,exea nufep declinans. Hoc opère ftatarmilla S V M, in fuperficie meridiani mun^ dani.Porrocontinenti operefignumB mouca tuf

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o P B M A T f 0.

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tur cx s ha(flenus,quod gradus foil's conceptus ad diem fuccedens quartæ V R,atungat pund 5 alritudinis compertæ. Hocfitu arcusmeridia^ ni VAE,notât latitudinemIoci.Nuncad nume rosumbrarû Palladq accedamus.Opushicerit utfeioteres c E diuidat in partes v i æquas, ea^ æquilatatio transferatin planiciem c B.Ita uete res ufi fuerunt,tancp pedes v i reddant fuam eu iufque menfuram.Èrgo affumatur ex Palladio umbra.Efto hcc meridianaad menfem decem brempedum i x.hæcredditperfuperiorêope« rationem altitudincm in quarta F d graduum x x xiif). Aflumat ci in fphæra noftra par ar eus meridianiex w uerfus v,fub hoc uero diefol decum't gradum fagittarq circitcrxix.Isgras dus eclipticæc c D H,ftatuat fub meridianuin lt;nbsp;in notatam altitudincm, amp;nbsp;arcus A E v mendia ni, notâtlatitudinem loci graduum x x x i if Ad hune modûfîoperemur per umbras reliquas, debebit ex omnibus fîmiliter prouenire arcus AE v,parhuiclatitudini, Sedexperienti in relie quis,ea haudqua^prouenit,quin ut feeundû quancuncp umbram aliam,tanquam fuperios rem experimentum fiat,reliquæ uiciffim adean dem normâ non refpondebunt: amp;^ licet depre« ■henderec|uod promifeue arguant latitudines locorum a Carthagineper Siciliam, percp Italie am,ethuius ufq5regionemVenetiam,ad quan tam diuerfîtatemunde potuerint affumi urne i. K * bræ

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79 CANONICA SPAAS R XS.

bræ,tauquam uni climati reipondes, nefcio,quot; nifiindefor{àn,quod umbrgauthoris cum non gqualiterrefponderent locis diftanubus, emen dauit in eo unufquifqgt; numerum,qualem uni bræ præiênu pro Îoco conuenire fentiebau

CANON x.

DÈ FICVRA COELI, DEQVB tmerfu a-occultaûonefyderum.

Figura cœli eft difpoGtio ipOus, utæquator

amp; zodiacus,ut^ imagines et ftellæ fingulæ ^ueifî:^ ßnt conuerfione cœli fub confîderatioü ne horæ præfentis. Ergo foie uel noeße ftella ali« qua coUocata fub horam ex uerticali amp;nbsp;altimdi ne,reliquaomnia,quæ defîgnari incœlo poG funt, funtcoordinatafub parte cœli, ad quam peruenerunt:uidelicetalia ad ortum, aliaad oc cafum,aliacp ad medium cœli, autad alias poß« tiones particuIares.Siccaptatur rario ortusS^ occafusfyderum,dequibus fuhttam multaa« pud authores.quorum gratia hæc etiam adiun gemus.Heliacus ortus,{yderis eft emerfio exra dr)sfolis,ßc ut longepræueniat folem matutG no,uel fublequaturuefpertino.Heliacus occagt; fus,eßfucceflio fyderis fub folis radios, ßc ut in cœlo non compareat. Cofmicus ortus,efl:qui diurnus:etßgnumcoßniceoriridicif,quodoc cidercheliace priusdiximus. quiaenim in par te cœli cum foie fertur, oritur panter cum eo, quo cum fertur:ut, Candidus auratis aperit

cum

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o P B R A T I 0. 97 cumcornibus annumTaurus.Cofmi'cus occa fus, fydcris eft quo ipfum fimul cum foie ocds ditSedSd cofmicus occafus ed, quo fydus occi dit(utpo teapud c horizontis)foleexdiuerfifîî ma partecoeli(utpoteapud R)oriente:ut, Ante tibieoæ Atlanridesabfcondant, Débita quàm fulcis committas feminaterrf .Saris enim fit au« turnno cum fol efti'n feorpione. Atlandidum autem radix condituitur in tauro,didante ex diametro àfcorpione.Non polTunt igitur abs fcondi aliarationc,quàm quod defcendan tfub horizonterdefeen dunt autan tunc, cum fol ex aduerfo orit. Acronydus ortus ed,qui nodturs nus,quando fydus emergit apud R horizon ris, foleex aduerfo occidenterut. Quatuor autums ni pleias orta facit. Au tumno enim exiden te fo« lein fcorpione,pleiade in tauro,ea non prius o# riri poted,quamfoloccidat.BtilIud,T unenox Thedalicas urgebat paruafagittas. Paruæ nos ftes,non nid ^datefunt.Deindeneqj noxurget fydera ad ortum prius,quàm fol occidat.Sagits tario autem, opponunturgemini. Ergo fole oc cidentein geminis,fagittarius oriri fub hoe tan porealiararione,quam acronydtenon poted. Hanc uocem corruptam in chronicum libello nodro deSapheaadmonuimus.Iidem ortus et occafus apud authores fæpe mifeenturrßeutfus periori exem plo plciadcm uno tempore autum ni Ouidius oriri,ucrum ab fcondi dixit Vergili

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n nbsp;nbsp;nbsp;nbsp;CANONICA SPHABRAl.

US. Sedhæcuarietas Iecftorcmnonmorct,qutn aduertat tempus, quodpoêca uterqjdefignat: poftea condpiat locum fob's fuperecbpricafub idem tempus, deprehendet^ ex infpcdtione S^ motu fphgræ,quam fol diftanriâ,fîuealiquâ,fî* uenullâhabeatad concepts fydus.Secundum ifti quifcp apud femet ftatuet,pro fuperioribus definirionibus fcnfum,ad quem iUifuerintlo* quuti.Locum uero imaginis ud ftellæfingula* ris, qualem in fphæra habet, fi libuerit in cœlo quocp defignare.Corredo fitu fphgræ,ad linca cardinis admouebit quarta alterutrafuper ftd lamin fphæra. Index quoqjfuperquartam fias tuet in altitudinêcontaCdus ftelIg.Secundü hoc 'dirigat uifus,quâpoteft fieri correÆHîmepro lndicationeindicis:itautpereius^ceritatêcon tinuus radius perueniatadcoclum. is perducet ad imagin ê amp;nbsp;idcllam cognatam :qug quo certi or affumat, obferuet uicina cohors ftdlarum, quemadmodü huius aftenfmus, configuratio nemfimilemeicohortiinfph^ræairumptac.

CANON XI.

OB SIGNORVM ASC8NSIONIBV5.

DVO circuit maximi in fphæra æquator Si ecliptica, iugate afccndunt ddeendunr^ ad horizontem,fednon paribus mutuo parti* b us.Statuât en tm exempli caufa fignû G, eclipo cæinhorizontêapud R,^ motufph^ræ cancer totus alcendat in fuis partibus x x x. Afeende* runt

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OPERATION

runtfimul gradusxquatonsam,plius x xx v. Statuat akerius exempli caufa h fignum brume in horizontem, Ôdafeendat toms Capricornus, Afeenderunt interim grad us gquatoris non in tegri x xxi ip Ad hæc exempla etiamin parti# bus reliquis,circulus unus celerius tardius ueal tero afeendit. Hgcucroincqualitasacciditcclb pdc^,non pquatori. Aequatorenim fuper fuis, amp;r)fdem polis mundi æqualiter mouet, ideft paribus temporibus pares ipfius arcus fem p a# feendunt, ficut id oftenfum eft capite de horis diurnis.Sed ecliptica,quia diurna conuerfione fert,non fuper ,pprbs fed mundi polis: ergo illi euenit ingqualitas afeen fion urn, E ft ergo afeen Go figni autportionis ecliptic^, pars æquatoris quæ fîmul afeendit. N une eins afcenfionis ali# quas dicemus ^pprictates,amp;prioreloco ut eue# niuntfub fphgraredta.Ergo fiftamus eius utru quepolum Aamp; B,infuperficiemhorizontis a# pud figna M amp;nbsp;s. Quartac eclipticæ ordientes à quatuor fignisc G d h, haben t afcenfion es fuas pares quartis affinibus c e d F æquatoris. ori# unturenim utrinep pariteringradibusxc.Bi# ni arcus eclipticp,Slt; pares fîbi,amp; in diftantia pa ri aflumpti, ex aliquo quatuor fignorum c G d H habent afcenfionesparesîutarcus duogradu umhine l, amp;2 illinc totidem ex G figno, habent afcenfiones uterep pro fegraduS l 11 amp;nbsp;femis. Nunc reuocemus fphæram fub clima Roma#

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CANONICA SPRAERAB.

nu, quoniam tibi PauIcBombafi defti'namus commentarium hoe, qui Romæ,i’n hac luce or bis terrarum manes beatus.Medietates duæ eclipticæ, hæcC G D,ilIaD h c,habentafccnfio nés fuas pares afFinibus medietatibus æquato ris.finiuntenimpariteringradibusclxxx.Ar eus eclipticæ quicunqueaflùmptus in medieta te c G D,habet afeenfiones fuas maioresareu af fini ^quatoris:ut arcus ecliptic^ ex c graduum xl V.habetparces æquatoris coorientes x x v ij. Idem arcus habet afeenfiones fuas in fphæra obliqua, minores illis fuis in fphæra rcôta,ut cum eodem areu x 1 v. cooriuntur in iphgrare* élagradus æquatoris x lij. Arcus eclipticæ qui cunquealTumptusinmedietateD h c,habet a« feenfiones fuas minores his aftinibus æquato« ris, ut areus ex D graduum 1 x x v. habet afeenfi onem æquatoris affinis graduû x c v i. Idem ar eus habet afeenfiones fuas maiores illis m fphe« ra redta, ut cum eodcin areu l xx V. graduum cooriuntur in fphæra reefia gradus æquatoris Ixxij.Secundum hæc dicamus proprietates, que communiter eueniuntutriquefphgræ. Ar eus eclipticæafTumptus à quocunque initio 8^ fine, afeenfio efus eft porno æquatoris, quæfi« mulafccndit fupra horizontem:utfigni tauri afeenfio in fphæra re(fia,efi:gradus æquatoris x x x.etfemis.’in climate Romano gradus gqua atoris x x i. Afeenfio cuiuflibet areus diuidatur

per

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OPERAT IO.

perxv. exibit hora amp;nbsp;pars per quan tu tempus arc US de cclip uca aßu mp tus afeen d It, u r rau ru s .ad ^ximumexempta afcendi'thoràunaÔCmi nus femis. Arcus duo eelïpncæoppofiti ex dia metrohabent inalterutralphgraafcenfiones fu as iundtas,pares afeenfionibus iundtis,quas in altéra haben t, ut cancer 00 capricorn us in fphæ ra recia habet uterque pro fegradus x x xiquot;).qui lundi faciunt gradusixiir). Cancer in climas te Romano habet afcenfionemgradusxxx v. et femis. Capricornus gradus pquatoris xx v irj amp;nbsp;femis, qui iundi reddunt gradus Ixiir). Omnia punda cum gradus in ecliptica, tum fteUæ fingulæ habent afcenfionem fingularia punda æquatoris,quæ fimul in horizontem ueniunt:amp; horum denominatio eft quanta, eft ipforum diftantia fuper æquatore ex c fe« dione uerna. Indeconcipiuntur afcenfiones redæ fingularium pundorurn in cocio, qua« rum in prioribusfubftellisinfcribendisamp;con cipiendis horis fecimus tam frequentem menti onem. Sign um oriri rededicitur,quo cum ma ior parsgquatoriscooritur.itaquehx ligna me dictatis c d H rede oriuntur in fphpra decliui.

Signum oriri oblique dicitur, quo cum minor pars quatoris peroritur, utfigna fexmedieta tis H C G.

1 CANON

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w nbsp;nbsp;nbsp;nbsp;CANONICA SPHAERAB '

€ A N O N X I I.

DE SIGNORVM DESCBNSIONIBVS.

Z*^ Ompertum hadenus in alfjs excinplu ed, V^ut dier vim et noeftium magm’aidinc,tn^ æquidiftantium emerfu 8lt;f occultatione, quod quxcunqueex diametro fph^ræ opponuntur, habeant apparenrias comutatasteadem ratio« nenuncquocp,quæ recte afcenduntfigna,ea« dem defcenduntfecundS rationemjquaafeen« dunt figna oppofita,ex diametro uidehcetobli que. ut cancer defcenditquomodoafcenditca« pricornus, nempe oblique: uiciflim capricor« nus defcendit,quomodoafcendit cancer, nein pcredle. Hoc fit exemplum unum pro omni« busjundeintclligatqugfuperius de aicenfioni bus dicta funt, eadem dici de defcenfionibus, rationibuscômutatis.quare expofitionê banc ad fuperiorem reijcimus. Tota autem tractatio afcenfionum dcfcenfionumque,fufcipiturred* dendæ rationis caufa diei diuerfæ, fiue apparen tis,fiueartificialis,dieiquemediocris,fiueipquai« listquæconfideratio eft perneceflaracomputa tionibusaftronomicis.Deindeutcomperturn fieret,quomodo fex figna ecliptica: æqueem er« gan t fupra horizontem,die longiflamo Sc bre« uifttmotfexepdefcendantnoefte æque longiffi ma atquebreuiftima.Qua: uiciftitudo amp;nbsp;fupe« riora omniacolligens, fic exprefta eft carmine Vergiliano: Redia meant, obliqua cadunt, à fy dere

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o P E R A t I o. nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;»/

derecancri:Donec finit chyron,fcd cetera fig« naNafeunt prono, defeendunt tramite redo»

CANON XI I I.

DE H 0 R A NOCTVRNA, ETFIGVRA COELI.

T? Ligatur ftclla aliqua infignis ex acron y ci è J-/orienabus.huius notet afeenfio reda.tunc obferuata altitudinc amp;nbsp;ucrticali, fub horum cô munem fedionem ftatuat ftella.Sphyra fie cors recela,affiamat fuper æquatorein hemifphærio non apparent! afeenfio rcc7agradusfolis, Hic ipfe eft in horis noeflumis ad præfens moment turn. Eft eodem opéré con ftituta figura codi fe« cundum orienria amp;nbsp;occidentia figna, ficut alio capitecomemoratum eft, Altitudinem conue« niat concipere extrinfecus per quadrantê: quos niam oculus obferuantis non poteft fubireins terfphæraniamp; quartam uerticalis, unde uenis retuifus pergradus pares quartac,adfuperficis einccrli Sóftellg. uerticalis autem percommode accipitur uidelicet index transfert ad quartam oppofitam,per fummitatem ciusindicis ctmes diurn axem v uerticis tranfmittitur uifus,amp; ap prehendit centrum fteUæ, 8^ notantur gradus horizontis, quibus diftat quarta ex akero pun do M uel s meridiani,quodfitamborum propi us.Efto uero exemplicaufaex s.ergo quarta al tera,quæ eft è regione ftellæ,ftatuat in totidem gradus ex m . H oc o pere ca quarta ftat in uerrica li ftellæ,hge ergo fub èam admoucatur,et prgfis 1 x nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;xaeft

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»4

CAN. S P H AE R AE 0 P E R.

xacft figura cœli ad momentum hoc obfemas tionis. ergo afeenßo reefta foil's notâteius pofitt onem in horis.Hacratione,utfphgra tarnen fit collata ad habitudinem dimatis, fieri poteft ob feruatio peruerricalem folum,ut non opus fit alucudineconcipienda.

CANON XI I I I,

DB DISTANTIA RECTA BINARVH fleUarum in calo,o-binoruin tocorum in ttrra.

Slntftellæinccclo, fiuelocaduo inferipta m fphærafecundum ^prias radices. Tune ah terum fiuelocum,fiue ftcllam reuocemus fub V uerricem, per alterum punctum extendamus quartamuerticalis.Gradushuiuscomprehen# fi inter v uerticem amp;nbsp;notam fecunda funtquac^ fita diftantiarecfla.EftoexempIum perloca duo affumpta. Romæ radix longitudo x x x v q fe« rè,latitudo xlq ferè. Conftantinopolis radix longitudo lvi,Iatitudo propèxlir). Diftantia comperitur fuper circunferentia quartæ gradu umxx. reddunt in fuperficie terræ fecundum didantias notas nobis m cew palTuü, qualium 1 x M.pafTuum refpondentgradui uni.

Tota opera tio coditus apparentiü rcrum,qua^ ta puenitex motu æquali cocli, transferri hue potuit:fedquoniâad comentationê Pliniana feftinamus, quæ nos in reliqua plura uocabit, illue rci}cimus,qu3chic plura dici potuerun t.

H E M I«

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HEMICYCLI'

VM BERGS I, EX lACOBI Zicglcri Landauf traditio ne.

Emicyclrj meminit Vitruuius libro ix, Hemicyclium(in quit)excauatü ex qua kato, ad enclima^ fucafum. Berofus Chaldæus diciturinucnifïe. I Itud ego cum pro pterBerofi nobiKtatem, tumhune Vitruuq lo cum illuftrandum tradereinftitui.Defcribatur in abaco linca abc. eius medium pundtum b, unde educatur ppendicularis tanquam æquas tons femidiameter, b D.ex hac refecetur B E pros ceritas indicis.indeerjeiat: recta E F, quidiftans ipfi B A^etcentro E.defcribaturquartacolurifol ftitiorum,contingens figna FD.exD fumatur arcus D H in diftantia tropica, item ex H ueniat ppendicularis H G,fuper D E,amp;centro G.diftan tiaautem h fcribaturfemicirculus K M. is diuida tur in partes æquas fex, amp;pofita régulafuper bi nas fimiles partes æquidiftantes ipfi k c M,noi ten tur feediones in arcu d h. per eas amp;nbsp;E centra exeantredhefuper B c extrema, quæper H e no teturfigno L.eft B L totalaritudoconceptihemi cyclij. Definienda etiam eft longitudo ex aG fumptamenfurafciotheris b E.isdiuidatin par tes æquas tres.deinde extrinfecus in abaco dus

1 J catur

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«y HBMICŸCLIVM

turlinea, fupereaanumantur partes fex cquila* tanonis B E. quibus adqdat ipfius una trium, amp;^ fines notentur fignis A B:hæcerrata longic tudo. diuidat in partes acquas x x iiq.Demum aptetur lamina rrea érafla,S^ perpolita,ficqj in«5 argentetur, fient defignariones in ea, amp;r unibræ

multo illuftriores. Perhuius rotamlongitudi«: nem ducatur medialinea a B c.feceturmedia in B, indeque educatur p pen dieu laris d B E. Pofl accipiatur diftantia b l in fuperiori fehemate,et transferatur in laminam ex b uei*fus D amp;f E. fie transferantur rdiqua punda:hoc, proximuni ipfi

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BB ROSI

ipfl Ljakerum ^ximu ß .Bxhisfêdi’onibus du« cant gquidiftantes v i ipfi A B C.carum denomi natio interim differamr. PoftidjCxfeclionibiis xxiirj.fuperlinea altera a B accipiatextenfious nius talium,ctcum eacquilatationediuidant fe cundu totam tongitudinegquidiftan tes dug ex B L diftantia dudtæ, facto utrincp initio ex d b E.fecundu idconcipiat per canonica operation ne fine fapliec, fine fphgræ apud Proclum qua Utas diurnadieifolfticialis,inhoris 00 partibus æquinoC^tialibus in climate fufcepto. Sit h^c ex empli caufahoraru x v.ergo fuper unadiuifa« rum,fumant utrincp ex linea d B E fediones v q et femis,8d notent fines, fimiliter aflumat quana titas diurnadiei brume borgix.pro exemplo fu pcriori:0d ex eadem linea d B E fumant utrincp fuperreliquadiuifiipartesiiiietfemis.Binifines hincamp;hincexD B Eaffumptiaungantrciftaue nienteoblicp fupergquidiftantes ipfi a b c.Hg habentrationemportionumhorizonris,quan tumipfius comprehenditur à tota dedinado* ne eclipticæ apud figna oriends Sdoccidenus. Tandern puntfia fimilia fuper a^quidifianti« bus iungantur rec^tis parallelis ipfi medig D b E. Super etiamportionibus horizonns refecetur tota exterior longitudo metalli. fuper fuprctf mo margineportionti horizonus fcribant in« dicia fignorum zodiaci, fuper a B c hie -y', illic jj^,fuper ^lixioreamp; fuper breuiore'^,amp; fuper reliquis

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HEMICVCLIVM

reUq[uis,(ign3 reliquaad priorum ordi'nem.Ca fttgcturquoquclaticudo laminæuiddicet,line« is cancriamp;Capricorni, ducant cxtrinfecus gqui diftanteSjfupcrhisrefecenturexterioralaininæ. Bafis dicetur,ubicanccr ftatuatur lamina inba fini, linca media d r e inferibit x n,qijæad dcx^ tram contratuentis i ,que ad finiftram x i.Sic fc# quentes reliqugexordineharumdefcribenmr, Fadtis his neceflarijs defignationibus, reducat lamina ad abfolutam rotunditatem, hoc eft he^ micycIiumBerofi. addaturgnomon.isaiTuma turparipfi B E,undeueneruntex quartaF opa ralIelæinterB L,fïgaturadangulos rectos fup« ficiei hcmicyclq in comuni fedhone B.Huius ex amen eft,fuper duas fectioneslineg y' ÓC -^,cuni Horizonte utrinque extendat régula ad huius lineam, qu e per médias fcdhoncs ptingatfum mus apcxindicis:dcindefupcrharumcommu ni fedltone, aiTumat diftantia xquainterutruii que fines fuper Horizonte, fie index corredfus firmetur . tan dem fidatur hemicyclium fuper quadrato ad en :Iima fuccifb. Eius rei caufa das tuaturdimaad quod huius ufum paratumuo lumus.Edo idud fecundum rarionem prolixi* tatem dicrum prius aiTumptâ graduum xlq. Ei accipiat in quadrante fuperiori e F o, parar cus D L,8diungantur redlis F L,amp; E Lfedroans gulo exidente F,cd cuneus e f l norma,fecuns dum quam quadratu ad enclima fuccifum cors rigas:

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rigatur.Eicuneo parctur extrinfccus m mates ria folida triangulus, par fecundumlaterae F,, quæbafis F L,qui catheais,amp; LE,quefubtenfà redo dicitur:demurn ftatuat quadratu didiiin fupcrius,qui fitpcrfcduscubuSjmagnitudinis eius,ut large capiat ambitumhemicydq.hufus bafis fit A planumjhui'cequidiftans B. Atfrons notetur c, poftica o,latera unum E, alterum F, omnia figna in medijs umbilicis fuperficierum pereasmediasfupermedijs fignisA B cD.dus cantur quatuor redy fe fe mutuo per fumma ca pita excipientibus.hæc uno nomine dicetur lis neacardinis.Bafieiusquadratiftanti in planis cie^quali^aptet fecundum latera E amp;nbsp;F,triangu lum E L F,fic utbafis E Fjbafi cubi in una planis cierefpondeat.Angulus autemEjn angulum fummum conueniatgt;hic ubi tres fupficies cons curruntlateris,pofticæamp;; bafis.ficaptato trian gulo,ducaturperpIanaEÓóFcubi lincaE uSe cundum bas utrinquelineas,refecetur quadras turn fuper refiduo ad bafim:ducatur per médis am planiciem dccliuem lineacardinis ex finis bus quæex a Sóo admargines perueniunt,fus per earn mediam efjciatur ppendicularis fuper latera E F. ei decliui fuperficiei fuccifæquead ens clima imponatur hemicyclium, fic ut fediones heg horg x fikrede indent fup lineacardinis,illæ uero ex v i utrincp fuper orthogonali: index ue ro exeat redus fuper reliquaparte cardinis. Sic

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Üvai^^uani.') aan ri alt;/lixyianjiit,ïit itfarxi. Aixi^a A v ffv^ai// rav gant ]taüs,liaïr0iy\ ia airaa amp;t iaiiA vxfa yiftyaiajinan^yrat raUa .Pi^ff ».un;^it,piAiai\tlt;iTji»t aroiSan aiifiai ta.à J aanaif/,Tt aa/OialKit aâà,oi/ukf/ A Wl xAiXfitïrrJiit.Ait K^ ai ttaMii Ï» j«f Mytifz, atun^^tyfalfu a^t at,ah *à at^aZtJi wxaüt,i Sa/ua .inaf/ jon ar^iaaH sfi^.aiißfo^viia^MiixTS, Siamf »j ai liainiti rif aStadt, arhlui rilt Hl iw ^, aflilt taraaSa aan fixxfoi yiafiSaliriTai.'iï/fHrtti Aasiiïfi aViait 1» raiavra. Mtrxaiar'LTxi.'ifi'iTXsf'.fy Tai.aïaraftajy^,pitfifafiai.'.tixt jajp rav aiafiai. araniTixa! rgt; aafwaftai, av ê fil/Oafi axaafiai taofxytiSaa, Ai s^« aitmit ri ar, “a'i unaat. avAtnan ^ mf«gt; y/f ^e, rav fiMaaraiffrcat

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ii^arSa wpMXfiisSxxXp/ Ojuipi àntrji, ix^arip/Ti/riv^orTix, Jhifutvpy^'^i xSrrs ^ ifxispp j^xatti^piis,-^ nv is KiXiW itsriKla jTPiS^ lui «tiöii Uit ftor/uiiuxpux^tMV Jlx sy^KirTmof/ tp/ri xiamp/ i!miif\ir.i ^ Hpiiamp;nas ètrap» Jk^usts.^» üsyarep^.t^ a!’fiS!XtVj^7t''yi srP^arpta ^rat woixtimv ^irTtarriKipi y,avra saltayes ItaXfi, £tuu Jti fit/r iptifis i;i[igt;vtxi, ^xtirfßifeipfitsniifi JhlPttPürt.

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ApxTii apsa Tfc^^-uti.) mpi TßSpiop/ iriMir,SpxT0i apiarpo^pKpip/^'n'ypitiTfi y«ti. dji :ßp rêlr apialeu àrppsaiâxaap/, ^i-floi Jiiatiir,upniii/v^ Nai'XPtirs tv f-t^TÜ] dl-.JJipaivT/wixairopa, amp;a: flis i tP^s.Pnyi ) rlai ihiisrppa,èMrct Iwiis ^, ills «pz Ka»ii rtStUns aryxi’r yes xp/ Tf Api's,uidh.imSparstitsj' avs f^ffvranlSxn nj « Itvixp/.:^ y 'irp,va ^|4 'dj^^ipap/Ïy'lp'. Ti An hatnorrat,’) A:^1 fXffippiirifpprT! i:p\lip,ats,dlf fit ttxPiïrrxt apix^cu. tij /p ixidKÜs ipr tms lAoïs, iMPastavaip/ ii^Xhats apta^ea^ hilx^iai Seri yp^p^jx sp' s^ tropdqt * dlfypxf-.ip y ip/ SKxripi) aMi'h'epr 7i,xp 5 pt/pus. pvptis y XiV i èpa.i /^ èp’ xpxlcs lugt;uasaptafx ÿItXTSxlxXHtipi,-riwpit a,v J TTiipi ? apxlfgt;,v tÜptsyciltiltu, lui pisT cxi'yppi orppiatd isiiKiiP', HaloApt çifti AvxxsrptSvyöIspaèir, tqsp/ Aps KxAta lixlaixâtxp/^sxiiâtpissi Apnpa dips till sr-.pi jasdxpxs iyayip/tp/ppi tt vpidiSy.fSxpStapi^ gt;axiAiPS,Xj xAif ptivuttpiTSxSp^pfSil'Pa ■ói‘xpT'ns\sp fiimpi, sipu cpyisddtxp' t/m Apnpupi, IxpiStPu avTXp,«! S7P1 TiXdp/ dpxTPp 5 txpi^T h.xpó'st^xipxxAx. itap/ jipW Ppi, ixpsfÿàfpu -if'auwfiicppi ntif, tg

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«^ 7« jy ';tS|V St afia^at, tmitIuj rif i to^M!x.v\',ovcri/v.t Jj^rè t^^ilf %gt;ifta « /Halkin,TÜji/ j’ttrafuf/astftifr, àim ipee }tüitgt;vafX!ixfi(xigt;i)fi'Miuiif, TÜf/j TfiSfi T»t nfSi, à irri fV/ti, S a/ua^m hïyoi^eu^ J^efToafja ifi^S}wi, xj Xf mov aft ^M ft?, » OfTUf iiri /uiSs Jiiyirai.fTi xj Î snSf^Jlvo flt;7iijfi.lagt;fi'ii!f^iigt;u'xti at fix^x l\i}i]iUfiï -^iTfla à^'ittàftâlHt

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^ jUnoi UifXXiis.yiTri rxt àviixxfi ia ^^cTxs li’iipcoixt quot;^xvai nifx/xfAfxt, 'ix tniTas airSfi, at A^ixp^ot o ypxf pixTixci vxSil, ritlutxXxtairrapiTt^t tltiiii/lixi^i^uv itrisfifnidai, axpxii fxiifii/ti'ittp’, ipüffi ^ BI ts/uyifttSip', xf *vxnanrpit ixvrat àpxritpxftiuuxt. « ffi ï/Jr, xj axi/iisit tiiyijxi^fw mx ^ ^silvffxt,0oSpii0p/luia0»i. Ü'in •fJiu lipxmhp/.yi) Apamt Tiiïav“ cot xpix, xj aomixcji/ aas SiXxaxt (sy, «AA x^i fitexp) fUffixif), omp iJtiipi ^^ mix ri (rtpifivSof xl}a^ hinx xxipip/^xj ex BxiSxltatfi'iTs^^iiei^'itm, xsijat^ml mes axpatayei^ at iffimpifvaixüfi JlaXiySpSpet, ei axpv ^^ pivS^ aianf't h'it' J!i/Kft.iniyxyiivoï’ii'7tci incp/iA isspiti lAiixyiuë^ xyeji ri àfifijîirgt;\pip

rtt, i j /uJSet ßtMrai reetnxt ipema rfxipiixiiixi ifi Kpirf, Sn riu mppia tpluf^H Shpi ieoxTies ep^nfitalftnA Atgt;t rxi,lw ip^é/iwaï 01 luipvfxmt, txJ oa ^010 wxinijnif /d'xióp'-.i^ap^yatSxIt pomt rif/lipepefi, Alxrd.) t/Uxrept axpmeiepf f Kptrijt, aTujeiepi / M^f ri IspiiTixoJ ipet,ip6x ^p/àfivxi'e Ait npSfiot, aapa ri aapaxaptiipeii/ tx« à pet xyvxit, ^;tilt;/lip'.')Tip\t ypafeai, ^(iJiili/xiyaioie^axpa KenJlov taiSép r\t,fxlfX0i'Tet,rtfii/ua ye euyxïf opH amrvxpafnpaipiKpHT^rpxflüiai. aj xA/ai irip/epet sp/Kpirexiymof^ault popi Jhxfixiilp/ ri apxypaelt;l eina^Sptipp Sn ttèrip' Uowleprx /n'xla 'f wiiÂ^ «7» «Tr iTtpat ap;iït,Sp\0t y^iflcpi i/m ne xerfS i}x»niypre, xj s/ü pefnirip^^

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Tllibfiifi, ci AiKTiüoi tufirnt,f^irifi.y ixahiov/oiiijfli’fuxfàfi Uvaci/iivfafi, Jlf tiu Tit oefSt ifitiiTiiTa. -rijti ƒ tj* faf iiu’iJai, Jl^ 70 ixianidat. r^t *»1x4 An aät tUi oifàfi iji^, i Xfii JlfToili KicSai xim TiiirovfaiiiiiflucTifo^lib air TUfi igt;iii)/ialô5^,ùt i XiUfi Siif^haT t/»« jlifiäfinal. Tiif/AtiTiflaiiXixlu/.y tÜi fiel loua AißaAii SfxTOfi, iXixxa hcOKiJiri, aaf à Tat ihixas ni mtfoifàt eearit. fialart /f fj« ritmeifofàt A lwniaoofat,aT\ xànufiluf/livra harà TO ft(}iä@-, »^ xvrtrovfa, tnfi I troxoiv i¥i|». * Ali mfi Tofi oxof/ßiftio^ tviMpi, Tiiiii)(gt; ov/n {xinlui.TiXfdfioa tt ixilwfii iffovri ifxiovnt,o7roigt; j^x rat hxSt itttSfi, nyovf if ill'll fr ^

quot;Th 1/1' K^x ^oivtKis Tsria-cuiot urc^aaxrt S^etKxtxrxif, AA’ « fjiXif üxdx^HyK^ t7ri^xlt;rx^lt;u iTtiuff, PoTliH gtMVOfXiVH iÄtKM Tl^MTÿg X:^ VVKtÓs»^ ri /' fcTfcg» oÄiyn fjitjif, KTXf vcunHO-iii x^itup»

TÎ A ’ Sfa, poleixit Tf luworovfa.Aiii taAi Tf/utxfS.ßfa;^ia'^ovra,i/tiÜ!S ecarS ofifiTat,tuil lt;(iifiSVioigt;Tnti}it Kilt ärrvvm!liic,oi TfXaftmiAon Qäjuvt A^à'^') àviàäiffif/'^1x070onvofi^ A .i'ff îniaifi7» mvififä fiélu^ taixXiivfiivii, oiix 171 fi iurevmflctfillfri nxtrififit. oi livfr foi'vixit àtàxfifm foi ta voanixa, mil iuKafonfm ? s»« aaf',6aff0iivTitaafci TiiiiXahrußxi Kcuri. Kj ajua o iVfiTiit «Örnt Bahnt, àt ^óivixat àvalyi to ÿ/vamp;.ol ÿ ixdiuilr, yi àyrur'if tnt filxfSt ev]it,7ifàt tUi î Kixliu ofimt,àt/uti{igt;va Aianhmriff, ttifraimc i Ofnif©' ihi'xairrat liOhii, it it mTÜi Toitanat àraiépoirrat,)}

Ai hiytmt, tllài TO Am^BÓxftovt iffrit ïnhLuai.ihÏKiirrat liah5eSat,âfiafTcilt vovri.aapSivcv ‘^ 70 i7t!Bi70fr.

n»»ij faivofiivx.yè l!iSfiiyiBi,i»ia if hOfinxAsvi. Ts Ai xponnt tóp vvx70t, ai irmfat fiirlf. iuBimt ■^ AviairTM 701tihiov faiViTai, gt;i Ïti f^i ■^ AiSht, itXia fuBtfiifafruiA f ihiuvlifvi/Klait

H Ai uifii ihïyii.')i ^ taivóriivfa,5it fan ^ ihiyn itifr, iftvi^mfa /p.Teh Ai vav7ihtftlvintiTiTiiAtiimfa,ig ito flfa,07iihaIAii‘isfiifK)gn7ai i^ aifi fpfa.cuti ifiiAai/rS sfiffftin,érrvt oroAótXiifr, ai fuyabilur AwviVfOo fàfraoiovfiîvii, xAl aimthavirafiToi titov tiw liXf, üiifia^af ihixt, rit

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MsATfcg« y»^ T«y(ïlt;r« Tt^^i^irta sfocpd^ty^t^ TÏin^a-iJ'^iviot i^uinxlx vctV7'i7iiOVTTU. ♦ T«ï lt;Æ' lt;/li iy.giO’ji^CtS , oÏh ■B!O7CC(JiO(O KTTO^^xf , EÎAa-m, i^yct Swj/^cx, J^^KKuy ’snol 'r «mlt;?lt;t iXyaiC tAv^t©'»eu. t/C K^a öi iwa^f/s iKtten^di tpvot'rvU A^KTOi, ^vaviov 'sntfvKxylA'cvcu. wxtwaw.


Tàc J Jli à/t^nifas. )im «iT Jli itufmfaficwT3f/ 0 ^olKUf/ ftlidTca , lüüais ini TUdfMis.iV tuOiliTea p ToiiS ixiu/i0ft0t,i on Jlix^e^li â/uforifoett n0ta/n3o,y vxpaSd^ft 2® T007\VKX^ irw rif woja/iiuii/ vJlarufi T^t ^ri^ct K0VT0!ftiy,.e©-, njif/Toir^ X HmoJlov {lOiOiTKC çcuri.Tiu.iMi/0s yàf to/omrott Htfi iiiixa\ J^axom èiaai0^ luim Xif^i rt'Uf ixny/Moos tun ^KUf/ us.irot} t« HxnïOiV^ ^MOirra orora/uofi ärojuan, fiStiHfij ajtnx«0i. ^eix«i0 j iros^'oio at vS'h\liaX/tos,liaB' inpstjl ra juïxaçp fiaaafiTajii \aa\óJlui0.üi Xo Whos X* gt;w,« 'aióintX^ii0!araifiSaswSi'oi!/.

Avofftt} w OftKfos.ynxiafis lt;(hf/ As0((01^,0^01/ iji0(ioia t) ànétvovfta.

^iJifi'ü fAya Siü//u0t,')tat'vnf?0'gt;gt;lih tiOiftTsës af ^ fiyas, auçori^xt Xii^at iriTat a(KT0vc,^fiTtu X a^ei ToS Xfoi» MOTOS xA hfunKts fv6os. asofa sTuoot TOS a OTI TOO Itf 00011, o^Kos •toXa^xöasAt etuTof ^isif^«xooTafi\'niu0fitart,Tat X TfoipovsP.safKTOOS^iwaTtaTitoasrf vonifa.f^Ta p aaf^fiiaßäfrlitißaaii Maf,'p ovfßafiatjTä, xj rais Tpofon ififxTixü io^siia^livxyiV.asaflfV Xm o aonfrxs, ÏTi iu\rtf OffiSil «t i^* xoora, atrt,//^.^«!^/^«.^ ^mu raft ^■n, aoi'nov\xA ras ifxroos xA^f^ TasïfXTssti\xXxafko0S, quot;ExX’äfOt o'ifforiifiis.}aiTioy.sifXT0i xxar^faS^f eunov 7Ït aaéftts ^f üx^xoif fv^atlol Tiu.fóoxt ^ eiXóoovgi,Jj^Vfi^0‘l'* ras if ^ßofHonfa,

AvTKÇ fl y K^IlU pSy ViK7H KlTOTétVi'nU 0V^$t h Titbit Jè OS-a^H TT^^ipViTOd t « pXv Ot «Xg« OvgH •5r«f £c.ilt;}ixKtni iKiKHS cwxTrivi'ndK^K.nv » Swag« ƒ’ lp kuulxrov^x xâg9 tj^a. « tfè 4«t’ MTiijb EtAeToa Li^xAnp, 1(0« aï TsrotÄoti^yynu K)ßt5 -Ex s/T ctSrts ’STXhivi^rci (wxTpkyis. av pXf iKWH

Xvraf o y’ ^»[uz.) snfi jSf Xoo ifs xnif '0 yiyos. gt;iiy(i X\ o Xfiixaf, darxs fxf ySf rif if traf 7* ijjarij ootuiToofa nxoTiiuoyTtu. 6iaifaf X tUi twoogoos fxf,Ti avé fff on.ff7X/iovnfi, iiyovfhxff ßaoa, 70 X annxfO'tToa, yfaf^Ttli xn wiTHo^TOit, M aTroraovria . Uara ^p -rluj tifttf in0T\TXT0u 'o 4®*»gt;(i'. *ïr(»gt;« gt;1*2

2ti i ^ ifi mf! tIm loi^othlui f iyJxxs \o!f, i X aait fa onvxafßiod tiài rit Itvoogoofas Uffofhlui. 1» X aoXis ^iÿift tri i aorSfa fiaoi ifii0'if,«ygi “ mlt;3!t, t:xX' avTisv0Cx!o0faos,}x tadfa ç i| fif ÿi •amsfolfisaólistxfi.ojnf ÿ o wol MTW 1771 T0lt;J foßifioov rf ^aiuèla St 0t\f, it X' 'inris iiâxooTaiXitf,ao(xi

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l/tftiis aAtv, urn « Apsirffs iwJ rei ^xxjinoc faal, niiTty Âi 71 euni'fhTia, in 7f ^oufa mamp;TiOfißaiiei r^ Uifa kj^nisïfilKiliinj ffwafafigt;ia£tcif/w\

n^iußcJtia tÜ htniSoóvfaf a^fi tügt; initdiuf/ vaJlSfi, ara avin iii et ita* Zgt;t!tb i/lvaat, Bâfifi ànonTii'ini äs Jlóffif/t K^j M lafMlih Ï^d ^ 7tvi KtAat rw \iiymigt;aaifgt;.

Oió3'cu, 9vi/C o'm ^'i^xAHiynA'iiJtTmxia ksh^ »

A^Ak Zvo ^^0'^Xcplt;ltç,/vl) «f 0{jilJi.Xlt;rti/, iis tT ^Ivi^Sip Alt;^Ti»y ^Tn^ffi yd^ss J^airoHi TnAw^av »

AO^it/ fA'‘ iSl k«fH . ViViVTl C^ HJXf^TTXy iHKip A Kfluj ^s i^tKHS ov^luJ. iJ^xAa lt;â' ^ nxr iS-v Kou sii^ix, 1(0« Si^OTXipöio roe täi^ix vaxTa ov^S Kftf'P TffOV ioicpxAHTÏf VH^ZTIUy HJ^imf XK^M Mto-yotfToa /vlt;rAs Tt ^9« x^XTOAou x^»A^xi,

Ov mV iiidi/ii^ilysii/ T? aBflpa^ovA' »M^iiv, Sï}iVff l/i w! fiifovs eèJl'oiDC fyiiav sfr, à»à Btxt\ii imiv ^7rlxf^^^|'lll 1$ tJ ^«hui/Tiit U'ifiXhS ipxi/^-n isifür, triirrtyttf. fs^èy Jl '^^fii'a/r i/luflauKXt itiM! Tairo. i J( h^fadix nurev JiWalat 7x1, wi aixÏtifiiromtaft'vii fax, «hX ismf Ï7tïyt,viiTinvavaa df^aKfafrit cà,'ài TÛt i7lt;fxiic,asn xar s.iii n axft rif aifis ÏsaSi ra, n svfta rai tftfaxovt raa, xA a lt;/l\^ias Itforac^at. irn'M^Saaair raa Jls Tii^t,'X^yaël'ii/ux ax ra Aiha^ix xi là aas\(d.i7Ta^ytl7'xaiaovuiri xA t’iras 7aviasifaJltfaTd^av,‘^ Ai^iiai fAji©' «n . Mioyaariu. ) ca Jlcaeis xs^ iaara'haa Mxaialavaija ÜMixaas. tóiyavaa^i axara^x, àf^afàm JdM tis, lixra r/Cfx'taxiu^ii^af/aTaxaiaxyaM) tiVXXay,as''^M’^aaura7lt;Q' aaaxe f af au f is. \.xii 3^ y^aafy^ a If^iai^ uiaXM^V tJl^lnraa, Xj ismafiiSJliiitlw üfanaat

ewrat! as wJ Jlvaiia dfy.rca BaiHfi, « 4 Tdï ^óxaxr©- K\facxx, Am r r'xXfia ai aa rav ixyawacai, xA raJ Asra FiV aacJlai buKhovim^auevaa^y/Tf rav aifaaaiha Sixalt;l }iaa/u[xx,tr\fi ria/aiaii/ufltxèf/ti» 7(Xaf ,777' axfa/s rau uxiacav iJlaai/x Ïf ^rea. aa ^ haraJlimau, ixX aanf au ra'it uriin^fiTet/. ax’^a/ayaa 3b afa^a i^ Aad^aiv, a ^aais. vuiax “ tf^faoi i f d^alxaalas Icaaai ravra r‘/uifQ-,axerai xfi Itahv/ußä Stiff 7aa ùx\aaav, rainit tl ratf a»laa7as 'vmlalaavaa ,07rav iri Âaais xàl « iaaraTtx •j-aaavaif àatiixttf/f f/l^xaaari mfi Tc/a/Wtax/u^vaa/a vexafr, ïlyaav hvxxay. a 5 Kfdrxs faai/a, as Asi4 tPiaaviaaaafi'fis ó/ufan/u/ayimi^ ij X!7! 0/uxf@-. v/yvs-^aaKresxà’tt/uanas nat UWii/Sai. itru^xaaf ïXdaais i i/ui faiafâiax,ij nilrxiaâ/aia, aaaa^ait axsaacjaoàÂiaa risJttmasTi iaaraa Xx,ógt;^yas raat a Hfijx^fi,

'Tais lA' ednov /jtoy'iovri ^yAivcATTia xvJ'jgt;iïotKoç it/uAoï/^-n (jdiA ovTis i7risx7TXi i/xe^xiAop aTrèp, OV lA' ^nvi ^Ofi/fXTOU ^wos Tffóvu, xTAX/Xtp 0VTü)S ivyiyxlt;rt üocÄMurl, 3« ^ tevr tl/ yovvxxt icxixyo^/

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«•AINO MENA.


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OxÄÄ^öi'TJ ïoïKHi ‘ ^’r’ «/^(fon^wii lt;/tt ö# u(ji(gt;n/ Xêi^iKfi^ovreu,. rKwreUyt (jätM «TiKv/iS Kgt;i^9 d'^Oil tf O^yyluJ. HiOStÜ /' i^VTTi^^i kd^luJU Ùiffnfovtsûi/làs KK^opij^ a-MÄuto lt;/l^«K0t^eS' AVTOV ^KKaVOSSitJlCtV®', TtHI KyiiVOi/ fc9««t ^Hfjt ii/ibfcu J'tóvi/a-os, K‘:^6t}(0(üijiHS K^i«J^vt/g

Tïf i/l‘ixvTi)v/itiy\oim.')im n mift Ky^it. Af«Titóifïgt;i^lt;'f*^i'lt;»f' gt;'‘/^, ràftiiyvaojiiiia AAiiffiiei Anti lAi^t tà mfi / ri i/jfinomt k'i.foOiis An}itgt; t-.f', \KJctinilc Vf iniKatSfof M^M* çi ttattmiSfofiAii/laffKli, 5 X ttyat, tafM ghfiïit luftoSt ie^i ftoywifri njhafi geini o/umcit tWhMTOi, e xa0’ avref ^ tuDii'nATca. tv^KoraififOfiMifii /f %!quot; out fewä avyKKrafifïTia,ài9ià iifès tiu Jt sifim^’h'iTiei ,w'^i lihcilffits im lut Tamaif lfitfi,üc ant tikis Itaftartii/, m fi X T0V 9lt;/lÓMv T0VTCV,eiJliis tsof«ffca ÏJiViftf, àViàftifOfVfivyivuiMif/txôt 1° ^DaHnnf, ^0iw àvi/uctai^i/. cUhaloi’ Tl ^ ioixt Itara liii ilaif, niHu^f t^t if^y aipofotufot attifturov, omf v tfe gt;qHit.m^J rov 'v/yfvvaoi ßeuttA^ot AS l«i, ÓTi mat^tt wnraftwu igif àiffà Ht avrov, tiui ôfyifàf amf, Ïti /f oft t^a,!i7Av0;tilpifiKTi!teis. niât Al' Tf in^h .^lutfiiva vn^a^ai^f j TÏf tvu f «lÜ! «J i^olKOIlT©- 0 \ty0UV0ial Ï» At tfo/i/ T0V 010^0! avicv i^d rti aits\f00.

v j Alt;t[infi,mn0ain0f ^ A(0tK0t^ot, Jt'if êopil0Tlp0 if^anoA10t.c yi' Ajianaf, ß0f(i0nf0s ih f i0}-eii0Uii.v Ai^^iSrifcg Ai^aijfiaued r ßopftortfof. vij Jóofori ^t0yiT0iT0i i/tSt AbAalmd, i/tifff isafiwi0n(tsTKfiT0vtr0tpvt lukutif, TaAiliafi\fiidaiTa:00f(i0i, taAiina r\f0i, ra vorix. «n pif tpimtäs v Ak^i r\p0v ib r ß0fB0np0v. i Ai roA vravt t0tUÏ0iiffis,n^c Altitfias yi'0\j0u,cwT0v liçfiiS00saifa00f,r‘fUii0it0f t\ça00f’^ *tfgt;tif0fti0 Alicn'00s iwtra 6iim0f rgt;t àeiaAlrni l^vftmxSxf, aj!i(ir0 mtj U: * ntsiam fpit/uóavi/of, ris irr àftâAitf 0Vftif0fSs .rins n «tivf Byifaar f, rf Ïtahf à viiAlni,yaft0Vfi\tgt;i Aii00V09, V Bif ris iff0Allr^s vil räf àfüf ns A S (00/. lutrsmeisSmou At ‘vri /uim/uif ril Ai0P0a00 9Pt!as.v J iywot sSniaf^iaf ^ ityavls irxyrxA. t Ai0»ia0s avdit lilt At icyttvif, Vf âf0W0f AiS inSf. “0\ T Vf TÎf \(0f\i/iis ss9av0f, iyaiiif iiA îsAolof, vil ^rtlgxftf 1) ti0i/uri^f vr0ig mf if UIS' èfxtâ.tnyri yif èai T^xfrifii àssfit, il Tint àn0rtgt;i0Vfi Vf S\^af0f.

Niräu vTriSpt^iTtu LiKiiHMrog ^/ÙAoUt Nmtûo (jXf sîipxvos TsnAKfi. üi^xÂ$ ^t itSiv «k^9 ^KiTtfiO rSK^ Kitpxhlùj ClflOV^OV. fcX lt;/!’ «^ iKaVt/Q Avi^y}i7ncl)^«!gt;^M0 epxwôfj^oit o^ov)(Op.

Nir» TjrtfpiçsT«. ) jô sfi^Tsa , Tiyttu) tir)'mSria'amp;f!l0ifa0Ü,ii irrisfiif^ Tuiilfirip, AliKB Jutv^iitiKinAytisa

W lirn r0v iiiy0ttv0ifi tAiifilit0r0t,amp;igt; T0A\y0i00fW 1“ Sy0«t0f iAH^Kf, «f f iAari0V '^f Tt^wifA^ j lniiftgt;iMTi,Ai

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JlciitxMxœs lH}jillia waTtif, Sis n^s rà âfxjuim, i/loxâ ^ lusliuins/i i^ ôxha {(if^x^Tàs^^fifCisrHiKiii/. '^xiAa vàf UifsOiliii, ymi/hßas wctitiix ixsais ^vua/iwx,'^ /uîuTiîi h/ulf yi/usof/ «f ynS viy âyet.iiK m, f^ift S ^ «xft kt^toif soi iiiynSi/ati, -M UMpUfilui ßliim nu Q'amp;iiJ;iûV. iiri/aila ■yf « àipa:71» rSamp;ni Ü^v Tfü ii^simiy. aexTà A Sw^©“,

est »W y* WI fîfd.tïns Zi 5^ (extâ was ifaxTiXs iinoçnat ß%(xxamp;s.oi Z sifOjUilSia 1gt;i}svlt;ri//,cl j TairraMf/,chfiigt;i Siiêfif/, et ÿ âtfna.xXioi Zi çatif' cwip/i wp/t/ifaxTiiaSif^vt/i vroJA/ucvi/ia, inia tïiTrûyJüiV j Mnü sâ/n n^vjuaTt)ii/,\iri y» sivmasifra xÄltiSmisßäx^eiiy, msavrâ [xls vax/i âi^a/iW9, aM X x^ i^wa çagif/.

quot;T0101 Of lc.i^XhH ^0KÇS{jJiv0l^ «yÂXÛl U/I0t Et/ovrou, uàvoiyi n^ xi» J^tyôixbjji trihluifi Eta-607^0t Tihidon^/. KTKÿytÿiS OV fiX^X ïirOUf Ai'^H yo^ n u^ m y^im/i/^oijôij^ MyÂ9 A^’ i/jCTTHS ^KKêivM i7rÔ'ltCU , OV yc^ iAX^S^quot;^ gt;■ h^eflÔTi^M iTo^OS TffiTTOvâxTeU, Ss §X7i (iîlfSS^ Aiuiva o(Ii/.0Î'y0^. S/' iß/iivis ivi7rx^«^ùst Poo^ii/ i7rtÿÂi€ei^(iiyx Snoiop «iJ^i^OTi^oKrt lZK0ÿ7r(0il, C^^XA,UM Tt ^ Ip 3Û^HK1 ßi^HKis

’Tinotiii UiÇMxScaiftasixSs çxti.') iisürii :^ ol àftoi Tare xüi kfaxlüi aô rw 'ôvnSt^ôiUiTovtsitii. ai /f sois 0ftûvs nu7X àisaT''thlt;iiftiTXs,tx^fis Ua0^ “Snxpß^ itifi àm M,wirf ni. xs^t afi r^i^/uxm mX» suf, àm niv lt;Âi;tigt;/Uxxÿ, ci lt;âS ? fnsx nXttx/xô,i/Tasà/6nas \.irih'rSfgt;,àait^ ly 1» ifvtaf/xans. 3» ^ Ctsnnn, Ïam tiara ■Mxajurrfiirx]a,0VftXfi/^ià;tSf-.sîlt;rai.

Aii^x Tiixi^iS,')xs‘trii àufS ^xf ^fl!r,xÂr? Siî^V, xyot’tf ^ r/i'ipâ- X'iiffo Tifari ly à/xvi/^onea Sis nés aoyxvaiti TÖiviSiuafi iiri'xeiTat'XaftrrxAif/.tiôra j ris r tamp;i’J^^x, xj / Ttl^«lx0XT0s wdfât 0\0s, xj ras “ axs fin a fuyonas ngt;ixàs imlxr^. ItXxSs ^ dirifi ixiumr, Sis /f àjuvi/^«s avris çifcn ax-iilla xj tixrariei. evyif fmifiixXOfixpsi, A/xfonfai.quot;) à,aip5nfiia ^xaifi càf^SfiS rodcamp;sJf^oti, Vif! ipf Stitfi misvii x^ isf^siffiy.

0 A* i,«/^if. ) à A samp;oS^iiis àa^axüs AiSxovßatiiufi, à/jqgt;or'\fois fois iavri mai ifi juiya 6xamp;igt;fgt; i^faxafnitfiixlJu'a laxÂtratrU. ^^àeiPtf$ woAimiT» ifdaXiuaiißaiX0fr,^3 Ax^lSan r Sifa xas. EiAilifj xsit Imâ^’;^«i àneaniftii avaïf Afolrs, ai Aoxa àfifaripovsTaai mAasßxlxxmca rSifitaJf^v Xinrâaxff mav , àxxx fioxoïa ■pf infaia. ^f/ j in« fois ^ ^fiaxafiriafi Aoxâ fw.xfri/xi çauimd) axas rfiTUftafi.îiia aififix AS f^ avr/a EvAS^ÿ wi hntalfpfÿ Auxl/ums oiaifi \xaiiriaailt;ß«i,ii'iusai:iuxiii auTii» VfX^finésrlwi ixAoaifierus, à A'‘ft ftws'iViirafXfas ma'iia, araarptiaoia isnixihlÖxeiaf t^in mAi ttaTaftfsrX fa.o/f as aas haraifi’-.Ta^i mf SfSaiXa ftav xs^ T Sapax©“. ft^ya A Oiiaopi, arl sfi/i oelxxa ai/ê}x\fifX Jj^ sp/ti)-\.6amp; si axopnioa,

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OgScf. «T«f öï Oög;? 541 /vo ^i^HTtU ßiTKJfi^a-tif^ ùi^lTi^^OÄiyOS, O-KCUV ^i füll V'^'Ó^t TSOli^Qi » Kou /» oi siifwi^ Tr^K'cKÄiTDU KK^x yive/x » Ketóét Jè asra^fis i^iyx^xs tTniaiuto j^HÂàs » A Z\’ Ktf/Sj' lt;jgt;xifoi/tyn/lt;ilii5i ovJ^ii iyxvM, ^^óyrt3^iJ t/C iAtK9S ^i^iToUihaavjtioiKuf A^KTOifvhxj,'npg KVf/l^iSi'^Khiiivo'thoóir9if^ OWi^ KiJiXfcUVS i7TXlt;Jli)lHVamp;' amp;lt;/ÏT(U «fKTW , KOU l^ihx TÏÏ«S i^'^AlihOS , VOT ^có^« Zi 01 «JJTOS £ƒ KXKbtII K^KTOV^OS tA/WiTOt «(jK^xJ^oy KSH^» AlJtlt;p3Ti^0tiri Jé Tsac^tp ^OO-Ki'^'XM JiilTCV PX^diV0igt; ^»^^ ^X^^^quot;^ ‘Ï*^^ S«}(yigt; MyÄHiVTX»

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H dduoo!ixr efliji fHyatoio.^Ti^s ir^Aixso^bxi fftiKfoó Lvoos, 'os ItxOiS, reaTtfoKiiotf/jJisfTPWx^t^todamp;siirx tVOidf/, snf'i 010 pftfiixfOiO hJox iTiiKdz Tou KJ j yx’hx^i'xs.o ooit, 07ritdif iK 70V fdsla liuois éfyn VOUO^I^^ ovx t^uS: lüi twf U»Tx tH ifooif/, '\7sdMi til tü

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Kslisi srxAxrasp axfxafxpfssp.) 3= ssxAahisp Itfirm alla iiitsmt3isif«s tl rUvsit, Sri 's lisap f àfyît ipirpsAp rtsfOiyrai.Ctsjfliiasai A 3® rsxAariisp av T«s,atpf'sfpilspis«s sxis^initArirrfJft sap Ïja pssLu, «fi} ataff Aisipv aamp;fpi Ispisyisi. nfrRxv'ixpisAfsp'fAKp.') if^KapSasa a^i rsvürsvs^s rssafiASp Ïirspil’'tlt;i^luifa,«fl]irif'i ritasi/^spia A«s,i(SÏ! AiAxsxa avrs 3® Uir©- arts n tap rrfnyssiapwap, MW« hfiivr-l rap if^dhsip. 's ï ssss,TiM A isif^opfAxp liai rs\f itslit/ atf,arsvÜTsvssv(3:p,spat \«fsla .mrHusissp A, üi css7ifstAA\]( Isa'srsipLusiiQip^lsiirft, isn “pfXi aipaSiiya t Aisus. àmpfâfy ff «i si* afsfä nét 3® Uirst^w j rx fis fax riti si^ipifffa.

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Oà yapiiyt rxrayfnaaa.yaà -^ fiaf: faPiaJat eJlaXcv ixt itltfiVitiaiff/c wala araxxà éJlaxa ra -afaepafiua araara ij fi^üs Ksà liana rallia keifnaa,aave rat KvrataJlat ntyiyaafiiaaia rxfyelaxfi iJliJta^yfi aa/a ifiat an eJlafaxaixßiia at taa'xiaa'i raat a^i'atf^itif raâ Aavai^at ea. eaZi iltaix èJlaftxatiSxQtf, iarà rrpaepxfiwa,

'Efems siyiuvr« Tffcc^i^yiTcu. cdncc xtAi^S« AVV(iigt;^C»lgt; iTiOSi), ’■« T^tS Ow/^Üi/ OVK tr’ tCVTaif Ecp^KITXT fi(P iVOHO-ii^ KTffCtVT OVO/fCiSt KCCAiOStUf H At^ct (f6fppagt;(sgt;:ç. où yx^ xt /iwhOuvo Tnivru^ OiKTiiKKiK^ffiShaUitwoff ^7rêi(f,ovJ^/ttlwfu, Vo^^oi yc^ TffKVT^iy TscAioaiJ ƒ’ u^lirx 'ay^Asvrou.


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sriysurtpiTi ^ïi/ux iis^yale/uwofS.

7 a gt;9 ifmyipias.^Jj^sió/siw fiia'l sli eusiapi mills sis 1^ àp^ls siii Jl^svsraa tif troiKSsfUMiSfiJblifi spiny\pias xA a/ua srsidofxs miiaatSta xslj dj^sälai à upas, oisus tpt ƒ« gt;9' hasa sdluh 2b^9 W/SaMA i^amp;jMas xAf^’f^disns Ss stijKXSui.amp;hasip/ifiiii sa èiJixMji ssfeilpH/uipasaSsa sàtsapixdiiaffispi faiSwa i)vSfixsa.X3i ivpi eïnTi iff 6av /sari afas^iasKp, eJituavi'(i{ ^ Kcava SKSI / o^iUf. ssUXat ff siu i^ffi^/uiff n gt;9 lymiUif. K’ls/lia xx/ucal'ui’fl.^ii's '^sifoipx/uwts «sfldlsts, i sidlyTipus ^‘ss^ sas le/liasadsiff. sè A äfap,0i yV iAt vavii aanTxs'iJii'axA’iaS' Ï^a K^p^aua ptieofiSva/ióffili, iJTsfiatSffïiiasofUtA ys'iifxi,tt!stgt;ffyfiiyfi’/ÿf/om)f),lt;/luva* scfiKfi. Afih 0'1 ftf xaixpdigif/. ) vsi si i^is xasa sa^ift isiii^yainifi ès si srpa KafSfiff. axi, al ySf sifoespsptwi is^pils êuSifaM nus,dJlixsiis ip/tots/isjsai, xA ifilff fampói aai.sa ^ srfaxdpnxx asfx Kasanpa xd/maaf isriJhuxa/iyixSiayt) av. êmijSf /( ais iAiax'isxi, aaifsa lt;Ai exaTiaaxASsaaaafiasa, aifffiapipaSsji tx Seauaaiasi^^, à^X Stppxvas/hi arres. Jj^ si Ha aSsia^xA àssfafxyafUfsa Ïb • Jh’iffX tdrixf pdfiaxs} piSaaf avsüf, ssfa^l’iSi/ihla.

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KaiSiJl' iay»Klt;ifi@'.yt!r^'i TSvm tv ijflvM tllfitx/uSairii, us»; Torro aMiy lt;ygt; râfi TrftzyvuaiU^iiiii, lt;/liJlàfXlt;l à» f taymifitr©' i^ T«it t'OTûV afoâit. efe» ^a ƒ? MTiét ^iv i Tov xiyûKifUT©- i^: tôt. 0 vrac/ici i;tS«tlt;S^iv,i/uiyas x»*»» t^amp;, et UâfiT^tifJtxy’trea iJlief, à^ f rev i/^e^és yaïat. ijtov îiH}itovt tu Jlvo i^fSvt eff fiîy-.TCU. nbsp;nbsp;nbsp;Et liires n» efXftfàeamp;.')Tiîi'^o/ifgt;i7ti F ÜTeiî }[H àçefâlgcfi.Jlée ovfi JUJluai nxftie/et rît ticcTagt;iiilt;l’-.iit Kf rev cvy-exifeir©'.'^ A cdaférea, lin irfhät fifucu, Kpkv tiiiifoy \itiviZ’fi^/i',àimfi\r'i.ueitlefi( fxjv i^te/tf rïtjv oi^t/e tôt me ^àiiTes t Oiet ô» irfmfiiif/. ) (ff04“ ‘’'f^^w. *« va ni Wt/'i :;tjôamp; J^/Jacfifaviif, tiîav nait^ rf/àxojena,às niet ne nfOHfl ieirgt;vtrtfcfr!}nti F elet, «p rUftjeeJb

fi'fgt;,Jlxnat/lxf]rpû\yvaff^aiviffl^ lit» Jliaxâ Ujxnie.Uttievai A rit i^tif vine eniff Siinut, i În nét nfi ténifi/^ linxncf/, A»ei A fBofttiÂKn.yaôni^ Jlÿhan^ai'il afinvtiin à^fuit lidntjéÿp v îy en te, nw^i im à^f@‘xj [/fe }iei xj f Itxrovt. vexfietevH A a^Sn rtâ ni/v Jt^ tÜ ttfe^/x/nexp aîriav, vnv f ne ma tenaextitaiJi/lii/Ta avrit\fi^^ verte Imnwn. fxein à/e en àieiéfianl itei, liti:^\n\^ .y ßpac/cicxnii.^ovrtt riîi Icarinf^iv.àn^’tl^oi yi,!^ 70 «fx^ O}’lor\pevt,r A \yytii,îri e vJ^e;^@-t ;tn ceatef v/^âeie àjp äfften, óp ev iel Kefirf Itarte asiftSlr f\fevria,clt;/llt;irvf ^vv!n amninev/Jvei.ivSet A vj teSa çn vi,/!^ rat hantrat rin tigfienvon v/i lein, rf y teaefir-.. o er cc 5^ x; el i^cd i nSvet. XetfewnfciaceTtJlifii.ytn/fei

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Kqvm yat yp^ pun/iS i7ïo'4'i t/lvovn KiyovToa » H ? ûj (jJlj/ (/ituiavcrp(/. o ƒ’ owTios oyc/^p if/K/is, A^' iv/pJSp ^oipa , tv /^ «l/tifCTb^ourt^xeivog i^ (xOIÇ il^'llep, ^tipiOS yt in^/ iQj. ’Sfi7r0tSùg^ Pxvra ^i^ui/ Tsorxtici/, lit^xog -^XTaviTixi «fiiOVa ^ÿyplAptfj Ji AiCt/Ti,7K (jSd’ y^ wKfT« t^t^opTva Kx^Ktvipi ôigt;s' ïlt;/lvov7ti. t(gù MiTog^cd/T«^ Syi yri^ H {jôbp®'yCcJgM pS^ at/lÿ, «Tag yitxp tf^ isiót/lx Äeuep oi^Cù üv/ncuvcPT©' ‘^asp'tlt;lgt;s aïKixvota, At/n^i/ia /' vlt;/lg«g ^i^xAa yyxgo7rôg Ti^ayoïôg » Koï Tr^OKt/Xp , Tt^OTi^Ot Ti 7rÓlt;^^g liVVOg cÙ.és(iSjVOI9 » Ov iM 3gt;iigt; cAt^ovg y«Mg \:i!m véiXTX J^ceJAet rttfSivl^(WTi3ii0vQ(rAvÿf70nàv7ililiult;iu9y

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A ^TifUS IKWOI , TT^iiTi^aip hoy©', oïfutir t^^FT» t.ÂKHCrXiTiyb'^010yia , OTt 3N^IX 'mXt'TX Kx^n^os u^iup si§x^H iTinKO'^i ào^vvfi, G»f»S K^vv(jAikamp;' àavMyx^ni oivottiuvi . Hs/lbOlc/^ MJTStS iTmaVX'rD SH^tOil K7ili.O Nna-OV , CWX^^H^xQx /jcbtrxs bKXn^üi iiUAxVXS, XKa^TriOp. 05 jxi^lp 0V7X t(^ bKTXlfi TS07ih.CyiÓvTX PASOT^g©- TlfOS^XVaS-b^^ C^7i(Xiy HKXy^ M7lw ‘FOVUiKx/H1{^epXtrf’7I^MÓSlt;^b§}(O(itSjvOlO ^KO^TTICV , W^iuvx Tl^^SavoS t^T« (fiiïjyamp;p .

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is xstjisr^^^in osiso isxofni© asangt;t riüjs ix^olS, xssids Jlva/uas «}lt;{ny aV asa, érx 'vriya ßisifv/iäs rlw ‘issvaf, cftixivs on AS ftx aai^S)i,yi üf/o avail mnoiiß^.äf^iilii^ Ai ris «ssvxt, i^sofi* n'lirai tÜi afn/uiio , on Sf^irai 7\t}lt;!/i as vos à ii9faorx iêialii. xj iipoaito9 oust TÜfTiiyoijv^on jâf aoifiaiOTifuy^y *

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VV“I,’9 oiii^ftii, njij a^ï/^a asdas, av T» mnofllXl-ßlilip'ihi ‘^ IXTlOif^ lül h vimxii/, y Df/ sf3SViJ(n'l'iTca t/laxi/iw/f, STi oùX f^yu Siftnifi tx inxÜTX tityfif, /u«n JTi xdl Jfi^iiV. y^ j aJli « itosia ad as^f'is. cili/mtai^va Jhai/iamp;v 19 afidJl rxi VM! t//!lÏ9 Tf fXirf i!gt;Ki,TctVmßxtt ^suxf/. xnii iy^iot i;^ t^Ssa Ifmra^ät x^j^Ts aigt;M3xfigt;fgt;aèiüi ^,ê'etoïgt;amp;iif KhxSiim. nëndzui/ üi/uv tivmfaiiamp; *gt;tS^ iff ßmoriat o ùvay,àamp;stgt;c ay hu »xyic^ontit haiayx riff i^xamp;iif,ijtlt;igt;li/3 tv y Kara tÜi S/n/Uff luwxy»ovlt;s:/', axoiti fiss iSiélifi. i J^ lufxóxlu) 7X1 idiCiv arm »ft Jj^'^txywxt^iy àexlt;Âigt;Siv«i ^11/ irxtif f HiV, v^‘üu i deix/i/ üThxya^ ajriiASx^x) tarxiteloßii xdl av^Pi 19 5 axofjriamp;.èrx *^P ^ xj if ti(xx5 AJlmxùtaèiffi idz ^f,ia piarya.xdl gt;x\ ixSmxxxTxiftH, « nziuf lAaóa.en X Jluoa 5 ffxffin'®', • auitf ét/xrii^a.i ^ ^fNÏxxi'^ot,nt i5f Syüf ^n^axt yifnA»!, ßfx^uv n fx ipxirif au rif ffn^piTwf,lt;gt;llt;(xi'Vc on lx £f finvJïVXit, ,9 fixfèi af i^va kardyua {iruf. evri! fi i Afxr@' ix / asfoSfan

as liXTXiiiix@:s -p/ftyiS^, fxaif on xdi S^of 'óf os aióip(xl'^,'il'x diitttAo6i o axof ssi@‘, Qxfxs xfoof^. ) xyouu mfio mioóf^, aon UxsoMxcoofSfamp;idJ^ i» ^0 fisvafTXlSx^fifoitiO7rii)i'©'.fi} ms 1/1),uj yfifoii^axfiaiinl p MftSdoeif .its ddiaufltaTa JhxyWt^of roó0x0f Trio,

fi dli 01 è/i avrils t) idfTifusfxoifl ^ ounis d ^lov imraSixi àoaJloôiioou, ionsif iiroóxoi Sxüof «Xa, as iiés ra ‘iorx if rt^^ia, àf fóoof àfyâamp;i o ad» Uf. if ovfirma 0X^,3 fdfiTca KSflims ratixi. noxxif lóora.^ori yj» oifó/fa fiiyxsxfOüuaf^xdttixTanf Ofirfof i^isiftxSaf.ftiyaf ff pfiïyi6@- f mod Offris iamp;fii/laas. imifmof hard j» fixos ,imfifa ftiroiyilüivrófüeiKOx, xolïadrlfx rifOfxoas, iff axofrriof 9x00 ahaoox avrOv xsi! /ua^oox^sci^lifj^^cri xsót dUo xisfaf/uxxosiin^fXj i^xxooró» foifos ^ffoo©'. Slvuox orfi^^So» oos. )19 avifs arraarSf raf hi^iaf of a d^x ixitiyfxifa-T ovaoa MoixOTx,Ta f fis ï^dra lixrxxa/j(xoilf,-iii^So}ixf ft (ov xs/iTBi dlahixs t

CVlK [iRjÓ Mgt;{/l^0lxlc/lnS Hgu KH7i«5 Cot’ fcAtAST^O Karsv sT igt;wTt?iiOV'ïamp;' «ndhêidlf. k^’ e^'a KoUtTrt Pxvcrvlt;/li(i ^ivyavenij. ó cÆ ^iit'ti rin Kw^tv? rcü.xpiTU^veif'rK {jS^a!Kie^xd\,bbix«Ax'sr(icv7ce Blififaip MKiXVa'lS, 7« iT OV ^i/xts , X^K« 7« y cd/7CU À ÇKTBt St.Cgt;17lÜ0V7l Tffó/xe K^ yOujÙX »(5« lt;ƒ“« » ri t/é i(^ MJTH Tffxt/o{i7ramp;yi7«i esc/hf^sta d^eiÄH ^Xd7ii7rax. 7« lt;f^'‘ üvKb70t oï ^X7x àôx/xOif «tedî-tTKi tK e/li^^aio Tirós/lit K^ yS^iS vTi^S^, AZ?i’ My' àt ài^xhliv Ïxü /t/i7' i^od[i7»^i tPles^OfJÓivfi yovx7agt;igt;. t7rèi ovu x^ tixiXKlt;^ iKav9 AcoQi/i t(^ nrxvÓTnt /xiyxhciop «Tip txudxi^xt. ri /xÜ’ x^ ^{ fcTigWjp Çt^i7SU. 7K lt;^ veiodi fiX^op \ y * ovg«gt;«f

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Ovg^r#; «tT/^fegs, st^arö/oTt tTivn^« àvxAx Y j^^ts Ttlt;j(^iby • (Popiel 7 ujS\ ütpjrouj^oio ZüiJui Ti »(5« ^npx^u^ gt;nbsp;K0K Snpioy ,S y’ ^ij^e/pi ^.ifmpi âlt;ÿiTiiui^amp;' tj^«, rot J^ cu/^i yS^iova-i

0iAiiii/ai/4'’/*^'^f‘y'(((^gt;9'''»t àl/^it/AJlnt KS^fUitailS: ■iMâniTt^ 7* TSfi^ilMf/iiiaiiii wt TuSra Jlauo. rmf} lui^at T!(fi\)gi livut Jk/vn. ri fié ^ ï^S o» fSf tn^yf^Jgi ris il» KfifiWM eap^S Hiif/iihoi^.ijlüifi iilhititvió{mT@',ivTtyaf!liiii)n at/ irt^va. SfiiT0n i/(,an Pfi ifmxift tJiMf/,. navniAie(piiy)egitgt;.')i}tfi tuti wairri ^tUtitfi Itarayemo. i :^ à Wf/Avtfi^, wnv taMuft m AJlcKX tai, ra nftafxfi^a aurS aarra asja Aoxn igjifsalo^Jbi ntn gai aSgi He fi\Ta iiitii'@‘ liaTiigi,^ JteKrurSfif (ae(ti,Wluf(i,ii!^x^3S.‘p j inaiSidf, agx\jfl}t ly trpxfMiKtutjiüi.i/lä S ggStn,» n ij «uil ri^n Uit xj à igi^otaiJhi lut raAt/Uxagiv, KSigaèriitgati/ltt.y Kan ifMit, tg ifMar àM» i 6uya tfit ount ^ftrai i lutaiurda.e'i ^' ai At «tins ij Tayogara si tugfu'uc fifty rat, ixui axSgfiat. an lnfaiiliii yt A/t tdut Iw^isif^ JluiTot. Mufgfliyil tai/traft. ) xygau Aai rüt JUgiUs ftiOt ftfu^it tari ta yltata, « ^ ivlof/ n* Ai^tToi autit ra yltara, is ini raßit fdaoïrra, iatttvxafifUT^^it.yirtii Ai wdy^ à lutgriijnia ex ïfiiVi^ igilt;§/a t3iu,iij aft liaiKet\eanilt;aSlüitti räisext

f»fgif’,Sea)fny«ha!ii/ Ti/uitiSt/gt;g letu i^.‘llf'^tü aiTiat/ tclüriu, ij g s titra Jliift Su/im/uipt j» törgs Tf ;^fa aant, it iya}KaAïeai,60Ïe(ui ewrS afgeStai tiii àe^g/AAeft, H fii/, «f ii int flut fifvea, ) evTu ^evf/ i Itagnirraa iai Avg/tat lunayiit.yttv yrinfluj rif Avgif fegif. é A oi(«nt lt,aT!igt;Slt;jti amp;i fio[girr@-agfa, «»aUpTitiraret Air ^fd, itl^efi TayliiiiiaTtxia ,tàA Auói, 'SnfaegiS nA^^a ItoitKa,) iimTiAdnfei rriamp;tAoï.if/fWat'it wat r luifKÏvg//,air^ cn i afae©- Am \riii,igt;tül gvfiitruAi iyiOiS^^iiii Adn fa ItJxha.i 'urdAifHiKtgi// f^eMfz àt vi^ai, * f It^cu/ft gif a ifoini, ij A Sfugv auri Iw faeféf/.euù Aoni giuf ai'amp;anM^ iaSt fainrai, dl^iafi Aarr^a Ujiiha. t riri fegif/ Ai/g iviOia, trof/ Atulif Hj Ifjxitt, KSt; iraft fn^t t« nfamp; warixidii^ti ^ixèit AJg agi hu» a^i 1. VA^KSTi%ariif,')xs^riïieit tafrit vAfat.in ^ifiVfiof/at^iCiatàt in^ai, Sd^ aurifr inrMtivSi^u. eu5 A! nat ra Ï^ara fufgt;i avrit fegi duata (aiedf/, es^ roi iK/rraüfov 70 etirrif gS ftafAj^i / ItifarUt 19 rit A^iit, ifiA ieeiofi Itfarii. 0'1 A iftnfiAin viAt, na ftiuoy ffti^if/ withal gav irAf t

Tofoy iT^^fépS^TipOTipOl TsÓ/iS tTTTTOTCe ^H^Ós^ TÓfa K^ caret^ÿ olt;lif.amp;' x^ crSi/x clt;Q).ov}(?v AvnTttei iTnivri » àx^aaTct /' mj^s xyti^^ ZKop7r'tamp;’ xirTiKttaii, ewlt;iygt;ft tA' xjjtkS olt;Zf.ov}(OV Xs^xs H^ TTpOTi^Hp O(piOS IffOAVTei^®- XÙyUU . Tovyi fjJ^y ^yirxo-nz. ^^ joy T^xi(((iÜamp;’ «^

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*i nr xfinfis W 70^9 inf^oorxi, xn W f'^nf àox7x'^orTi, S i iifeoàiTiryi t«/aetfMàTisà»syis;tl^isfui Üi

fisf ànf}t\7t^ Tiu/ÜlsyitwiMt fif.'jtau Ails TsfoefxfSTjiois, istiffioi iv(x,siskôhx^isS)gi 70Vxliiovs «ri ^xà^Mx! ^Kwi àva7njx7mi. luixâs ^ nnî P 7ipiX((vn7},uatof /f sr^t)ié7x/^ teiAi XiifiTX oM7ißifix,a^77\ftx Au m3i,/iowi bJyop vxvrwit mV^ Ü’* vof/ W fûùlona.'fi ip stiivis S)gi,Att in rà ch^x ourrov SAv7X. HiA fsovofi ewri j» S)gi siSovSfX) Aie w ioetiff, K/uosimfs'^yii^io Isvult. ) i7iut» slowsx fHoiio t^ftetiaeîiMluTniAoiiit êsAvgiio fifOOTjfii i ifirxs ivx! i^i. fs'tyiroio 5 aelt;f7 àfsoifvyoamp;,J^ r/o aea ofi 0CV7S à^fx,gt;i }o toils aôftx T ènufoi AsAvxï, ttilvii / AliitjtefisÂv^)fift^ Vf^T i^i7gt;,7X 70V »v«vvs oras7x Av» ve/v^ootilib / A\liSs;^ifôs.xv7X Ÿ^fts/ie is ßofeonfX. niorx gt;\pàb aitMi Äi ) rt e^xoViitit f av7ov eoif, en xa yaos »i '0 UsK/s^aan 7rpoxsxT\».lt;!is àe r Xayaof/'xj TifoKonxAvvif) ,ujftxAi no7\ i7\fas'ij(i{e,is\f/ÎMi9,7è i «nMW,li tvlAi iXiV07\ liaTOta/uêaeXTi Wl f lut vis.tou yigt; halxâfitxt,^ f luuiis Aie eif^. MX s^ iviijfi Îf 1901.^01 Îfi^os tuil i xîf lutrà M 1^5fx fi violas,ax/ufia ^ }tifsivotftf}tif, 07Xfi utn vo^o Aux tift miv7t,ifilt;^iti isivs Aitnf, ⻫

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H't.yir^lw ii/i^Sfa. ) Ïndf' çMiin tiw ^Sfa tewtiw cf^alfhZf Jlg-^ofO f, trdst^ Iturèfi aifia n iiicf^cv. hata /p tiwiSafr iiaZhlw tüiaiyo!KffiTiii; fUf/.•^oM!:i^a^@■;^e!ft^t^l'J■lmlu. Kaic'i/u\gt;,iaii/.') 0'1 luif 01 JlÿKiiTiiioi «: fiH’ a^fH- ifi aâai Zit t iiici^ov asfa, 0110,01! ^ixafii Tt^t P l/i0«atv ^fi/jSi fa,ctaf.' atw Isiai'hi'a aai nàl ftafeiait!. ^oxü a fill ti0Cigt;ixSt.!.cv ff yifit^ Biixai »f/ns cayi: f^fiV^af/. ft^^ay ^ fff ifii;(0V,^eftèfi, oTi i^ Jcti/fH itSf Jht JiJfiafi Ottt'tfif idif, ໫ fafli/ ataf/i

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èhi iftfii xi/hi ini !” fanfa/i lt;1^111.5” A ci/uipoTifuO'jV, xyafil cSnUi acx^hSf/ ou t-M/lonxf/, Hlt;Aif i^ trorcifiov .^TOTb ■jifiir tcoTOfiov tifiTiw liocjutrlu/ifiltaa Baf lil Xffi àiJHa tnMyfi ticunii! àçofSff Ïcfici $10. ilitaTai A dl^ ttofofii oanafii if) TovTfiiiftoi/ofiiavTOVifu/toSii, xsit fa/ùf/ enin(idlx\aaya'Pfiiùamp;gt;iiia,néc'o/fifilt;t Insa atpepüotay wttioaaifi 0} inxÖTaa.^xiil JÏTOVcfauuii^-vóJlaiavTÓsl/it, dj^ iiïrio eevrov ifuxoSii. Ai-pfittóói) vafUjiia'f,') xyouaixi/l'i^if^. o!^ faS Tca^mavtJifaiBieuelfiaTasii/iiaTi toS ra ra asfa ntitafovndd, tij yaaXisa ip/c èeuimnxftxfaSi aoamp;fiintovxTPC ttrea fidinToaffiifot, Wi taélif/Jliasxftaana xhisixaaifi/, Idioorft j^ riiè t worafiov x Ita/utrxfi/, liaTxtioxlivaifi on t^iao/i o »s fiOfitti/aTiViei. f dièfim©' çav^vrof, yd^oTai zcóoif tic oiixtÓi Jii amp;fa, tear t^^ü? l^ifiaratiri ^ cvfatici.taÜTaT^ d^^ 7 asfdfi/nxftxvael Bid alSfi^aaiff gt;

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OÜ^ ófxat Jc/JgOó^flfïr ijuifi^xî s??!« fiiÿc i^fTniii T^pif. yj rît ’■»,i' ispuf haTaTtifpiUs f^yoy, Ïf^’-.TOiXtri äifioßit (jifoivafi/lpcißiu^'M!,'^ U^tMi} JlmirKs fttia,vjßojh’ti!) a^pi a'MiVKS J^aêHiV. Kip ypTovroiiitf tUs ff'^nt'iii ^apiart^ f HS^ K^ T^pT i/TilüU aH7IPÜgt;pf^ AlKti ïtptïfp öïrxt ipili^(i,uigt;i//.it/lo^i’/iinaifiiTi p cv^ opaxt ß irfiaxirü/i/ of, yrpos Tii’a apa fipïif, afos'ofo ApxTO! lt;ij^\yójj!f/@‘, 7if oo’/uia^iT},iyiiTiuJliif UoOtolipSfOf. »gt; pónS^f ^,0Ti oipi sotufOffapSf Ttoi,^ Jlflinpi! \)^iilS:^ Trpoaini, iamp;a otoikti xS id:! 007 a T gt;^}-ef\'jiiijuaTi'(s:^.tg Ofx fot, lod ' oun amp;f ßpiloOTa quot;Jlon, W 07X1 ^OKMiiTinv^vj où j lt;n6^ fii/ijtx'i.Jl^ fy ? iitruf iSostyfio^Toa His ^xooxijjii rolt. nbsp;nbsp;07tiyiiiuyó,')tir!lpxTf Jj^ oooViSf

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E«J’ingt;ifx0ayiYfA.')ypa^Tai,i lat vou faSayiyyit, ‘i tót a/iany.Xiy Itai vououy fxSayiyyiittsijsxyint uu ttü ym^y^^iuui fiït autüyiüy vaftyt ay, Uati luiueu n yinna ii/afuhi nt hyAiy iiitQ- wt nü U Aiii «rt/gt;^|Uta ^*' t^t^tQ-, i tifiAitm lafixyyii

/uyyaliai 19 ^ASui m/i tii itvifoy ■ftyBUTai,;^itySuaaiifiaii/tffiy. ^n eloittài/uâXny,') ytOyfy©- vaytati lx nû ifiltu nxyttia, V/Sayyihfaytiua eaaya, asti vxfaïuii/iSyiuyitt xli! ^ At^nxyxveis tfuty^'ly ry nüy.ixil Atayy tf icaixi (ù/ifafiya nxyn

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’S.Kl’TÏf'ci tlt;£^ ^XTvbu ^ » (^ T OAtytl iOlKtjCi À^Avï, S^o^^gü-v vwi i.ce^Kivlt;^ »yn^x^. A^iJi f/li imi (/Iv9 Ai7Ïfx ^CtetPOftSb/it (fO^lOVTVX As•fcƒ4J, ov7tTi TiroXKoif «7rno^ot,ovT^ ^taZ’kjyvf gt;nbsp;A^’ oirom (jikKisk ’orvyovxKy oina-x^vu. tas (jSIm Ro^^éteti, vórep a^ iTrnf^iToa oeJi^amp;’a Kairot (jtSjp ü.etAiov'm. cvoi. (ji,iK9 /i Tt (ftevvy. Htè i(gu i^xTriuHs uxowTv t/ltès ^/tKovi©* riviT^ «epegvTamp;' 0^9, tbi /' ipclt;p9'TÏ^lt;uQlt;^ tóvvit Astgif i?A»M)i/ cd/iot^/çy iv/xK^imo.. OvK oÄiycp ^afxivi Tart ^Av^^ptki x^ov^M »


^KiAo nsit tfinlM,) StafaTia rit ^ ^hafip^ f órini,iaiflt;igt;iiJlKt of ova tfofi.piafaxpi piihaàpo^à,àaâ)iP Tortf^oposfaxopaev UopHioov^xTic^^ f jifmftop ^ttcrufup ovra faiov iifOa fx)-quot;f4igt;Tai ,ati^W ^“f \xarifa 7Ïi finxt Jlóa aófis, i ß^ßifaosjt J^oiai it,mgt;[oi/ovt 'iiut}Ag^, ‘f^'p KapaxëióSau A fón^Hf. JliJlom ovp ipip \k tiu/tki / faroxt nxfiteia^^äros a ioupaoïos.

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Uf/jfifiti^rift^üfi/A^tf/, sie lip aafßtfisigt;.')tijo^KC Kvippßofera infteihp, i Aïi^fis veTiineamp;'»i^i ühOKivirjai ivüi,ivi fi^fof^WTip i fSanift, Hrtl^mfpiit.'iSrit^m t'y W vapT'ii^^s wsiit âiÂnis tufviJll-at agaric iii'^^‘o.01 lÜKKecT'-. pet afiaù liii i^ü einf^f aiui^Jtilipoi Muthp i:.vgt;!iMp farragiofi tslfiifCvgif/. irgp X au Ÿ^KTia, KSH P tA» ^dnluj Sfxirt THi )I^ Ä ai^iiiii:a[ Allias tugm^/uifi fitrTQ-jiafiätütiaiiäxiaii/umpyii. j® A cantp iiiro^ vyj’imtiifts ylraea i ftip injmaiSiitlQ-, xj ix »«f wa^iTKr« KilvyfiTinQ'iKai/iit ifcntil ovQ: lias ra fiitip àfuiJ^x,àifKm yinnu ,fiiaf fwsx ) reis siwt, in ä^anoÜTcu,^m VDiapiftlp xxfijtlt;{ Tov vhHffiiilpp i».i tus.e X nvt, \x/v fwipti tjlii ànfdr igt; gt;K i»iliMp fiavmTxi,ifxv»s ; i filt ni, Tiigt;iKctäTxß)ii;iuif^Pftätanftg^i ta, àrijp ifrî/ai-iUi firvlu' sfàiâi, nit A âniat î»-« ciMiMp fit ipJ^f pifiiA» ouirwt àifot sfSiiâoa .nsi^olcp fiAlnv fnTa^aXsvT©-ns viHaf, «V}i

tOiii^ïoSai y^ ^S jS fUn^S ifuatufM TêpJllvJlânif/ifUfiyitip.ifiel'as ^vap pnhatvvTai lip i porry. «i j âàfdr liai Tci^aunetiTM liù aùiûù Sigip ';ifSVTiV k(bs âiMiivs, uipnz TtftgJliiHÙ, vititp ffifannifnMmTai, raJ alfas ns ai rlà nsVia/u^ov. ià|U Arip ànfup hi vap,i^ß0fi{K àfiaaifcs fMvv!f,i j ri ‘nis'hafnctis,vmp tait vp(Vaaju^tp. ly iftirxgt;iip,ixp lip àfutufèt a vents, gt;10/1 'X^sjû Ts^sßeflxp,ßefi«fiitfeeM^av »rwefipep, K, làp ^Aias evgrs iJlfS tÜ çâri'ltu aupeiAias pire,un Iwàipa vi,tevt} ivti’tè^ixanfap fft^ip çai Ve/uspees gt;iaffirpas,fniap^ft/uSra stfog Maa. « i4i /lit âipaviis ^ ÿ^énrai i par vil, à»afMiMr,irai i ruses ,\fV hat nsiemrai. eî J^ om oiis à/uxvfei fait Perrai, ifiSfep ■irfetJlaiia,éeen èplpi^ eu fers à fame « tarni ^mSi eij as« fit lyyUTfep ivuiiiapfariei,;iBfjâps isreptifep Aifai. e jfUMira lipixaef n fanat'of,eiÆànfdr rii aùrü fnnp t^s ètsâilievs iieifP, vvpp afiti t/léaa.

£i Jé mÂMisHToa, yi; t/T (ü/tIk toiMTiS Mertp Astris «fa^OTsFOt, TSi^ljQ VeßctTt aH/aCUVOK/V , lu iT ö pXti tx üü^iO) ^KTf'«ï ifaimv« ifixeivn Ai^ifo^ iTrtt^Kviup. vÓtms J''' óvos Ky^ais amp;9f Aa/ty^cu ewiiaota vórovt Ho^iU Ji (aÓAx^H l^aTTX^l^ XyXvÓ^/JTlyffXC-lt/SlM'^ Ji^/cKWay » S«^« /h ’m ai^ijuia n^ ott/lMvevQx Sxket^x


Tij/Z^^üj, j(^ taxK^op ètt’ cuytx^si JiaócnVTiS, Akt« t’ avariât, ottot' iui/ltet H^Hia^M Ttyvav-rou, Itapvifiiu.'ri ^s^i/Sivou. ovfiamp;' KK^cu.


Et Aiiumatexrea .yia/fJÏi/uÏMii npiHcfiJliiÏ^lilriïijfiiapi fâm, gt;9 iji lt;41 lx rif rev at/ts ax^vras®’ ) fnrt, tl j a^frigip leiKintKvUt,


pixJi'iVTi v^i j^fSta/teaifivplpii,rm pufifiéiV tüip spitfaMpiipav. Ta’^ltf» Aij ? Jlffstfiirap Bt^diu: at aftaan It'ltAiihttTixitFiiffrAarQ’, EtA


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î tftgt; w ßefiU.quot;) T^ftmnf^ tari v fixitv ^•:jiigt;it,is\Ti nvSvmacvnÂfoiHtirt liiv^w, srafifti^uffi mSf/Seipel i^t mmeiûfi eurrâp Ssfoit aa^vpfets ffVea fis ^iKU'ai'vfiitiie^cuiTà j jiapufà 'an Jldiievil. avilit eipupi vuù, ixp^Hfip »tiKßafHavpifavnis forviisàiefâa ttcaifàt foiei, «pifa ms à^fhviJtts up, iAviTiosovasfoavnaa^tin iniminet W {«ra uvivaii^ap rp vérap. rà j^ tfà launî 5 Soip©quot; àvaitaMt, Tp vas Tiapieapftnfwr^ap uittainKi.r'pßaf iàp}itririifâp)fi uviovra ,0Tapip Ïp mhip rav èiiiiplt;^liav ^iiriu, i;ifviJlovt tip t/laMi/li T0^ van's,tiâpnavT© A ti ßafHav, ^«poii/li^iSvipota,')ù^ râp aifaviop gnp^up piraCifuK'jp àt ta -èsif ytiai, mil osi tifhts Sf^inu fat ^amt, iirâtaptctffvfip ShÂi'atiSfitt i Smaaaipitiustl«ta«,Kiîf pitxftvs à;^ tav xijuaiâp K^t âtranJiii^aeipap /â tipoaJlan^v.ûpoiut Xnsèi au ittinpi'op rit taticusKi àKrau, mSap rlutra f jirip i^ tvaai,/n^etat àvlfims a«poavovatp, iactlrutiXiiiài Srap ta àafifttau rSp i fSp^olài àrran'hiaip. àffiip} wp«^ raJ Itfarita rip iiti yit cai;^mtp n^s :• tapi via fvauamp;vras ivipgt,Tit6aßgt;aa tut, Jlutiou/li ipvaip iTTcetyoptjiif Hit Va Jluaip i SoOiatta, atpSip (tiisuSm

Kot lt;A' twuux^H^b^ ot' tg»ƒMf ov }^ ^ia^|Jto^^ t.f K^às i§X’‘'^ gt;nbsp;^^^ ’'^ quot;spaJliK ÄiÄmus^ KtwitSjtav xt ^KÄttsPsai) ^i^epû^ioir eù/iétat.


KalJl' Sp Iw {xfluu ar ifui/ltit. ) 1? nap a'ifuMs ix / hoiaatxt w» tIm ixfapafoiffaùfalup if^if,yivoaxi a» n ànpau luvavptpav axpHop irip, i A ifuJhis p if nap rap ipfif.up Ïf(i,v» »ifliipyXfalt,vni^ipvyfa‘itJlióyup, Pimâiut fvp ùrî l»gt;v»pxt lt;ijff^!fup, »

pup. KJ ticuyiaiMipiyaltfct/lovnuiKT Itvpirup ifliitiimt, gt;amp;) Opiifamp;euyiat h^ piyórist ßfipam. apafayS Jl\ n rfóvT©,fa^ë jp’iyx U?pa uori ^sfii intifaia.ai’pêatvti j iotvTa,Jlim àxfai çatiiiiytnvi'atns rav aifatiw ^ i'i^^ rmptrÿyi nftsifipïxim xpi taatp.éf ;(aplt;^avavpTovciifatxav^Mf(ip, txpu tp i ^ifot. XP] -yfpuaêax« pip ylviTea «ifat,igt;ilt;/linap^piyiiplp «läirrt, KPiy^é SatMora Jhailt;Aaivav$:,raai wat ^H luXTÏptl^afipSnpap,iSn aKrii i;tavaip, i /f tiettaa rSp avSfóttuv ai» iS risrav itfat Cuatinus oatStaip hapt (avfip,pa afa^St -iirafyavaxs.ipifl lis iftpait raai wpiriiHei, A ^ut èit piliiatiptrafhaixtt anaTa^a vifflvnt xifixiJtS^aiTixpxva vaxue;filpSeat tAfat©,irfOVM/°] f aeSfump .AJle XM alp ^cisfup xsfi fUiKvxt XP] Ma» XP] ntfarwt nxpi amp;a tSan XPI àtn li, yivaaxup ut ei;ti vavrilr aaif 'vrisii povd rip oifaviap, i^t ixeiSSi tg 81 tnatAaip^ai és 3» Ctaraxae {aviv ra vp oxfav^riiieix^fX^tixrüpvap «pit xsti pâiPup ipipyvutSp lép t^iJlaaxa tiiap vatitrai.a'ap, ut Saxataxt, u ^xt tSp^ix vvfit,i»liup,)i ^ aX\iip,xt\x Kanup rlui ttaraltixifip iplp vafi^n rev^^tpit'©.

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Kor Trim 19 U\,it^ot.yà:i hoivS F lu i't/u^e âif\f^tf iifii^ ToA iVi fn^èoftgt;»ô A fi{irf9t 70 opi^cffT'hinoffafKU/^ \9t,fff^ ^»■^ avrtgt;'vri\(isei i aaff, i^i Ïsift iàtf/fiineii/ fj^Mf wt tHyaXfi lt;K ogt;^fgt; ^ Ifntf i^i'i^. àg X ^iJluuu Za i» f/S. Ttü /f xtl} tirÜTcu Wtfi rà tlJlaj ta irxsf\f}i^otgt;, umfit Nixaf^©quot;, tn^fifXff if fus nfiu UhiiAa xarxoluvi gxfi. XirgAif tvfi aicSxrai Sjtîyov irritt fjiar©- vrfifi/uîVviyTosXTUxTai^n fiit ^ff î iix-./uaf, «Jd aojcv f in/is im JtfiraxK, Jra tmiey \Kfim,jm àt t» idji» f^s/jr^i^ axxxx avi Ütt jH^f lc. «^« iaài^wtiit Uijrfin. a y^ ixirpt ^^ iftr^, miâfiî^iiffT àn/ucfgt;.à, ramt^/jt^tif/ f v^i ^ aSfjia atni id'u fiff\x f àj\/xi,liaKit aflt;/iiïliS\ii.i/uû Zi àtri iifSiJ»Bamp; îiUxTaijjtt aAufii infitt,txi’rn aiti ^^ Zt^à^xj ovjtit » »lt;gt;«, ji tmvfta.ija^iit/Ki'anîei T^sx tirrvf iuXfiafr vpé^ ti It^nfti atixJia

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vÜitrjf, jsAti Uari tvsftiflùi Itarà àg tihltu lunSinf^ji n zrMa^jai aii\/u@'.

Evlt;/iiai BOTMiirii.quot;) amp;lt;/llilfÔt,f '\ftll Toa orog- TTfOMoSaifT! f âigt;'/uvfgt;,m Trxei fiora “toi, rin /? àtrixfiaunci f lt;A ft^y “jflarjf. fiptnai fi àyrurftgujtci, iaa^ loij ti !;^m, Jifèt infitf jx^îfA ggi.baraAxiei ygt; F Uü/ux tiii feixliu f )njtit/lamp;, « taipüoiis imp^fftetfi. ngX\a!K/ fi’àyvafic xxivxh^XKarati'toa àypixAxt rat iy iî» ritott J^^Xé^S sfeiixs gt;iiyg,Tas xrx/uifwt wi àyetat, jat ƒ xiS^at g/g àfx Jheat fiixi^X’^'l'^ fiiwsjif aurif ii SxJatirx •ijnynnjoi Tii fiim, ntmti taixirrifitfïfixj@' fefä. jovra im rit^iflcv fxaipgt;, graf Tifxxrxjxi ta Jlifa, infit/f gx/ueurg. f^iygna-^j txhaÜiefr^^ftira,-^ gt;( / ôxMfixt vyfmra inoliiygvgif, »rJ ■M ^t^fgagtrxfayixôiJfa, H r\f\7ii ipyiit. ) gt;4 Jett 'iti TÛg ifûf j fixxuvtiui fat f. filial, wgafixJts ox fxgi gx/tar

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«‘MŒMiJ î^ aui’ai ntfûiKH ïtttJliJlixti tuna avKmtiy fi if st. quot;afu^ X in aim itOfSfai nifiMt 'urirms TcSf/cfSf/ia tfufoatt iircariH/tirrai, iw «if ainfiamp; »1/ivQ:t, iiSiiaif ainic. i ray ovy Sri/utt if fur} JhaK^y titu nfijilu.' imKrati/i turriif/,m(1 Tovi nnfiieny riSnaiy à A fts/UKxavilrQ'Tid’nfihIu/, tiXti Of rrXmii hdvxv»)* axarSa i luM/u^ii tundfa, irraXay t/ixriMt, avowrai, i*fr‘yamp;5 ‘’‘driic, ^y iluAüJ/Uj aatrt nn.iyXiilt !rpalaMXioic;^xuigt;ir,i» aiiAxy crrdurif drx/u©-,t'i aamat Unvt til 'imt xA watlbi i IfvrUn, ndt ^ txiyot/illifuv axx^irrtfSyn^iynidltv »1 WSJimi, xf iinnXitnilr Xitti eaiy, tri axiyi luirioinffsax/Kioyfiai'y, g Xs

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lt;^RODVLPHI

BRVGHENSIS AD THEO; dorichumPIatonicumjn tra duÆonem planifphærrj Claudia Ptokmari, Præfauo.

^j VEMADMODVMPtoIcmgUSjrtail te eum nônulli ueteris authontans uiri an tiquas fcribût hiftoriasîquæ cundis diicipiinalib.fciennis finis eft,ipia carundcm omnium prinapium extat^ naturæcomitata (èriem,cuius omnis ferè termi nus in originis meta concluditur.Quod quo# niam pracimus eft negocq, locus exigit ab in# tegro exponi, ut plane confier, quo nam prac* fends infiituti fpedetaufpiciumtac ne longe fiatdigreflio gt;nbsp;nihil prohibet, quin ad imita« tionemalterius translationis nofirar,hicquocp breuiter commemoremus, ne fi diutius imino#

remur, fcribentis intentionem fufpendamus. Narratquippe,trafado primo amp;uniueriali dû luuio,quando primum undis ad priorem alue urn reuerfisaridaapparuiqiènemcum filqsiu# perftite, cumex Armenia, temperatiores auras fequutum inter Tigrin Só Eupbraten defedifTe, êc in quarto climate,quo pofica Babylonia für« rexit,cÔfiitifle. Hic ex nepotibus eins quidam, films (ut ferunt)primogeniti,plane quidem an kquam nepocum fucccfiio longe à Mefopota« n- * miaetcr«

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miæ terminis difFunderetur,diuino nutuçomlt; motus »primus fidereos curfus,fcquutuseHc« dus,mirari ccepit, à quo paulatim fequentis a» taris ftudium in orbe deriuatum,eo ufcp accre« uit,quoad plane demum deprehenderent feien tiam,principe loco in gemmas diuidi ipccies,in, motus codeftes, ÔC motuuin effèdus : tan to qui dem interuallo diferetas,quanta eft inter difei* plinale ftudium amp;nbsp;naturalem fpecularionê dû' ftanria. Quare eius,quæmotum fequitur,omc nis uis SC ratio,in numéro, menfuraamp; ponde» ree5ftat,utomnis mathefeos difciplinæ,ôô pri mordialis 8lt; finalis extiterit caufà.Eft enim mo tus ftellaru bipartitus,in eundem amp;nbsp;diuerfum, quorum alter accidentalis omnibus idem,alter proprius omnifariam diuerfus,atcp eidemcori trarius,uterlt;^ circularis,ut necefle fuerit ad cort cepri arrifiefj conftiturioriem amp;nbsp;dimenfionem eirculorum,amp; habitudmem mutua,motuuni diuerfa proponi ftudia : quorum, quorria pri» mitradunturautores Indi,amp; Perfae,inuenrio» nem Ægyptij quoep fequuti ftmt. Idem ergo motus,quoniam eftacquabilis circulifupcrccn trum, amp;nbsp;axem immobilem omnia conrinenris fphæræ,(èorfum hune feribendum duxit Pta» Jemæus: quippein ipfo tanqua ueftibuloaftro nomiæ,quafi thema quodda torius ftudrj pros pones,ita ut idem diuerfi principium,amp;ræqua« iitatem inacqualitaris cardinu intelkxit. Nee ut

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opmorfalfai’maginationeabftrahor, qu5d in omni cœlefti mocu,amp;m motus effèclu/fic eum autorê habet fïnefmitaöóe. Exquib.amp; lonica lingua duo uolumina coUegit,primam Theori een, alterum Tetraftin appellans,arabice dióta Almagefti 06 Alarbatquorum Almagefti qui« dem, Albeten commodiflime reftringit:T etras ftin ucro, Albumazar non minus commodifli mè ampliauitdn utroq^Só ipfe 06 fequêtes eum, illas diuidentes ordinantjUt quonia altera fub« ■ mota,rdinquialteranó poflït,nec conuertitur, lila naturalitcr ut finis eft difciplinalis ftudfj,na turalis quoc^ fpeculatiohisexiftitorigo,cuius’ prior pars fuperiorismundi, fequens inferior ris naturam contemplatur: id autem eft,mates riales rerum caufàs,quemadmodum ilia forma ks,omnisuidelicet genituræprincipiapoft pri mam ipfam caulam utrancp originantem,ut in eo qîiod de eftèntrjs inftituimus planlus pâte« bit. Cum ita^ motus quidê fit huius : effectus ucromotum confequens,omne hoc ftudium ab eodem mbtu redtiffîme inchoat. Quod era go ommuhumanitatis ftudiorum, fumma ras' dix 06 principiû eft,cui potius deftinarê quam tibi,quemprimam hoc tempore philofophiæ freiem,arq; immobiliter fixam uaria tempeftate fiudluantiu ftudiorum anchorâ quandam,pla neS6 noui etlàteor. Necetiam(dhs placeat)me, ut iners'uulgus folct,inuidia teneat, utfponte ' nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;AF ? quidam

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»• gt;amp;»NI«PH AB R I VM

qui^em aut mendaco locum præftem, aut uerf tatem diffimulem : tibi inquâ digniïïîme præ# cep tor Théodoriche, in quo haudequidem am bigarn, Platonisanimamcœlitusrurfus morta libus accommodatam. Quo faótum eft, quod baud aliter ^ aureis culmis Cererê, maturo pal mite Bacchû,unu te Latini ftudq patrem, prin« cipq s aftronomiæ donandum iudicarim: quip pe cû nee ego quo offerrê, melius haberem, nee tibiquiequa accepuus fapientiæ donocogno« feerem. Secundo uero(quod folertiam tuam mi nime latere poteft)utid al ijs quoc^per te inno# tefcat, quanta præfumptione nomen aftrono# mix fibi ufurpant, qui nondurnprincipiu eins ui derun t:quæ fine rebus prgmiftis ita poftibifis eftjuticarusuolarepotuittnifi his qui nouoin# genio,conuerfîs difeiplinægradibus à fine ind piunt,quitanquam negledonaturali greftu re trocedentes, poftpofios nimirum luminibus, cæcum carpantiter necefteeft. Tertio uero,ut quoniam tanduiriprimarium hoc opus code« ftis feiendæ, quad dauern quandam labor no» fter nunc tandê Lado côfert,antequàm in pro« fanas inddiandu manusindderet,tua fanctifli maconftaret authoritate. Quanta enim putas bominu partem hoc tempore fuperftitem,quae priuata contenta forte,non alienicupiditatebo ni ferueat,aut podus odio cotabefcatfquæ paß fio maxima Ladnitads inopiarn hue ufcp feeit, nee dun*

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necdum heet pereunte materia quielccs. Qum me quoq5,qui longe inter alios latere optabam, uftpadeo fopius impellit, ut tanquam cedens in uidiæ uoto,remifloç tanto laborc, potius ad commune quodlibet mu ndi negocium cofugi am : cum præfertim cundis iam animi diuitrjs poftpofitis,nihil praeter fortuitas opum farcis nas in pretio haberi uideam: nifi te tantumuir# turis exemplar habeam,quem nee labor uincit, nccdelici3ccorrumpunt,nec potenoffima pers üertit ambitio, iterum quot^cactcris diffugien tibus,defertaE,Só tanquammedijs expoficeflus Aibus,philofbphiae naufragium patiaris. Tus am ergo uirtutem quafi proprium fpeculum intuentes,ego Sc unicus atcp illuftris Robers tus Cataneus, nequiciæ licet difplicereplurimu po flat, perpetuum habemus propofitum, cum (utTuUius meminit)mifèra fit fortuna,cui nes mo inuidcat His habios ne diu differamus, ab ipfis dus uerbis tradatus initiu fiatuamus,non alia transferendi lege,quam qua antea ipfum in Arabicam Maslem tran ftulit. Fada eft tran sla do hæc Tholofæ Calendis lunp, anno domini MCXLUII,

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M« P L A N I S P H AE R-I V M

io fphæram corpora incidenteSjtanqnamcf* fet plana,confultum uifumeft in neritate feien* tia^ut quihæc fcireuoluerit,defcribat demon* ftrantem rarionem,quaairignari conueniateir eulum decliuem:5d circulos æquidiftantes cir* culo æquinocliali:paritcr amp;nbsp;circulos notos,per eirculum meridianû:06 quicquid intenditur, adaptatu ei quod apparetinfphæra corporea» Çogit ergo huiufmodi ratio,locomeridiani ci# culi réélis uti lineis. Decliuem uero inter circu«» los æquidiftantcs,reéto pariutrinq; diftantia^ quem medium fecet in hune modum. Deferi* bamusitacpcirculumæquinoélialênods A B G-D circa centrum E, cuius diametri orthogonali ter fe fecet ag amp;nbsp;B o. InteUigamus ergo alteram diametrum meridianu circulum, punctum ue* ro E, polum feptentrionalem. Nee enim altera couenitapponi in planicie, fpeétantcadhunc, quemadmodum in fequentibus cóftabit:quo* niarn feptentrionalis in parte noftra perpetuo appareat, is potius accommodus eft ad planiti* cm,cuius eft noftraaflignatio. Oportet ergo cir culorum æquidiftantium redo, feptentriona* lern intrinfecus defcribfauftralcmueroextrins fecus. Quod ut rede fiat producimus lined A c utranqjinpartê,ficcp decirculo A b c D exu* traqp parte G duos arcus squales refecemus. De fuperG H infra G N,côtinuamus^redisp lineis eu ùlrifqj notisîita quidê, ut D fi M lined A^cr ’ ' . nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;' ^üéniât

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P T 0 L E M AE I nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;a»

ucniat,amp;locum K affîgnabis, D N ucro m line« am A G, qua quo loco teogerit G notabit.Quo fadto, fixo centro ad menfura E K, fiet ci’rculus fuper diametro K M,fic^ non moto centro,con fequenter amp;nbsp;alter fiet ad menfuramE C h'ncæ, fuper diametro c u Diuifa deinde c m per mes , diüm circa di'uifioni's punefifi k, dcfcribaturcir ciilus admenfuram medietaus.Dico ergo illos duos circulos æquidifiantes,a’quino(fnali pa« ri utrinq; diftantia. Terrium uero fuper K cens trödecliuem,quem c m finea per æqualia fccat,. quoufep utruiicp iUorumattingat^alcèrum ad nótam m , altcrum ad notam c,æquinôêtialcm pâ* medium,quemadoppofita duo pundaB amp;nbsp;D intercipit. Quodutranone conftet,confis nùabis linea reda D M,ad pundurnz,æquinos étiaJcm drculum tranfiens.Quonia ergo arcus

Azæqualis eft areuî G H, qui æquali's datus eft arcui G N,ar CÛ ZDNjtofis uscirculidimi dium, efle nes cefTe eft, unde angulum M d Grectu elle ne cefleeft.Qiios, niamergocirs gg culus

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' culus fuperlineam C m defcriptum tn’anguluni s redangukim m d c drcunfcnbcns, tranfit per ' . puncflum 0,8^ fuper puncfhini b tranfire necef* ' fe habet.Confequenter crgocirculum æquino Æalem fecat per æquaha. Hmc itaqj con ftat in^ tercirculos æquidiftantes red»,eu duplicamus ex utrac^ partepunÆ G arcus æquales, quand* tatem eorù metiri arcum torius dedinadonis: quorn fines ubi condnuamus reÆ's finds cum pundo D ponimus, quas rdecant fineas rcClas de finea E K, difUntias circuloru quos circa een trum B defcribimus arrificio dad exempli, ut fit intrinfecus quidê tropicus cancri, extrinfecus ucro tropicus capricorni,attingcnds hos zodia d,æquinodialern per æqualia iècands,ut deferi ptum eft. Medtur itac^ (ait Ptolemæus)dt fcn* pdo noftrautrunc^ arcum n g,amp; c h parribus xxiq. pundisferèli.exeis quæccclx.totum A b G D circulummeduntur, quæpar cftdiftanda utriufe^tropici acirculo xquinocftiali.Qiicni locum a Ptolemæo minus diligenter peripeClu cum Albatenemiratur amp;nbsp;Alchoarifmus : quo* rum hune quidem ope noftraLadum habet, il fiusuero comodiflima transïario Roberd md inJuftnajLatin^ orationis thefaurum accumu ht. Nos difeudendi uerbi rarionem inlibro no ftro decireufis damus. Eft ergo hincindeæqui di ftandu circulorum, L C quidem tropicus add mis,K M tropicus hybemus, ex quo coftans eft

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P T 0 L E M AE I nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;w

M B C D ené mediûîquern Arabes uocantfîgno rum dngulum, conongentem fingulos tropf« cos, apud c quidem folftiuû æftiuum, apud M iiero hybernum,æquinodbalem per equalia fêa cantê,ac fî prindpio apud B fumpto,per A tran ßenSjad D perducatur : propter quod dedînan ris circuit’ partes, non conueni'tut fint æqualia um arcuum, fed quemadmodum in fequend exemplo adaptabitur, Id autem dico, ut fit« mamus principiafignorum cxpundis,ubifès cant circulos æquidiftantes æqutnoâialt défis gnatos,ratione qua docuimus,ad di ftantiâ uni iifcuiufqj figni acirculored:o,uteft in fphæra corporea circuit fignorum. Hac itaqj rationnes rit omnis re(fialinea,quæ per polum tranfierit loco meridiani drcull,dedudaper zodiacû in partes dénotantes cas,quæperdiametrum ops ponanturin fphæra corporca. In hune locum Maslemcommentans ait,ut dderiptis æquidis ftantibus redo hinc inde drculis,deducatur zo diacustamp;ubi fingulos interceperit, fignorum initia fiatuantur. Quoartifido ÔCfinguIorum graduum initia ftatuantur.

DEfignabitur deinde omnis horizon, quemadmodum circulum decliuem des fignauimus , qui non folum æquinodialem per æqualia fccat, fed ÔC zodiacum potentia per medium fecet. Id autem dico, quoniam defignari habet per partes, potentia refpicis gg » entes

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aj« P L A N 1 s P H AB R I V M

Gîtes cas,quæ per diametrum opponuntur in fphgra corporca. Dcfcribaturenimcirculus æ^ quinodialis ut ante, nous A B G D area centra B .dechuis uero circulus nous Z H B D, medium æqui'noélialemfecansadpunéîa Bamp; D.dedu« cemus dein de per polum E,Ioco circuli mendia rii hneâ redta utrinqj,atqj fi placet per Z a e H g; Di’copundaz Hrâpiaenua eaquæperdiamc trù opponu tur in fphac« ra : id autem dico ut circu liæquidiftâlt; tes redo ad hæc punda defignatarô fecent .arcus æquales, ex utraque par^s te circuli æ^ quinodialis» quomodoex pofuimus, ac fî eiTet in iphæra ipEa. quod ut ras turn det, cÔfurget à pundo E linea reda perpen dicularis ipfi a G^n pundû T uflt;^ in circunfe* rentiâ perducentur,deindelineæredæT kz,S^ T Ajfic'q? T H L,80 T G. Quoniam ergo in femi^ circulo eft angulus A T G,eum redum eftccoiv dans eft, At uero quoniâ quanta eft z E in e h.

tanta

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tarifa E D in fèipfam ducta erft, Só taiita E T in (ei plam.unde neceflè eft ut que Ricrit proporti'o z E ad E T,ca fît E T ad E H. rectus cd ergo angulus Z.T H, Conftatautê redus 8c A T c. Sublato ers go comuni medio,anguli A T k,amp;: c t L,necefla no æquales relinquütur.unde Ôlt;arcus a K amp;nbsp;L G neceflario squales relin quûtur. unde amp;nbsp;arcus A K SC L G æquos elîèconfcquens eft. Ex bis er« go,quoniâlineæT K ôt T L applicant ad arcus, quorum eft cadem diftantia à pundo de circus lo æquinodiali;quæedudæà pundo T,acquis 4iftanteQppofîospundis a amp;nbsp;G,perquadrans tes fuerint in linea z G punda z et h,per quæ de fîgnari hab ent circuli duo æquidiftantes redo utrineç diftantia. Quare necefteeft lineam z E B,continuare punda potentiadiametrum cir« lt;uli decliuis terminantia.

DEfîgnabimus deindecü:culum alium,def chuem, acirculo æquinodiali loco hongt; Zontis,quoufcp fecet æquinocdialcm permedi? urn : undepunda duo uthic amp;r zodiacus fe ins tercepcrint, potentialiter per diametru efleops pofitaneceflefit. Id autemdico ut linea conti# nuans ea punda,per centru æquinodialis traie at.Sitenim,utcôftituimus,circulus^quinodia lis A B G D circa centru E, zodiacus uero h b T^ quorum fedionis punda conrinuantis diames tros B D E.Horizon autem HAT G,æquinodia Icinper æqualia feeds fup diametro A e p,cuius

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ut F LANI B PH ABRIVM

amp; zodiac/ comunisfe Aio ad pü AaHamp; T, Dico ergo iï applicue rit pundu H c5 cetro E,Iinea re« da loco me ridianicirs culi,produ catur^ in diredu^ne cefTario per pundum T tranfibit Applicet ergo H E linea reda atcp in diredum,amp; quoufqj ho« rizontem feriat,at^^ decliuem circuloin pun« do T. dico itaeft punduT commune zodiaco quoc^ circuIo.Qiionia enim in circulo h a T G, linea: dua: (ê inuicem fecant A G,Slt; H T, eritep A E in E G,tanta H E in E T. ergo amp;nbsp;quanta B E in B D.undeamp;S B D 8^ H T in eodem effe circulo ne« celTeeftïquapropteramp;fuper zodiacuT figna« turn effe confequës eft.Fuitautem (ïgnatum iu« per horizontemtetenim quorum fedionê con« tinuat linea T H,quam per centru æquinodialis tranfîre coftans eft.unde manifeftu eff 8^ zodia ci inclinationem ab horizonte fecari ad punda per diametru oppofita. AdditMaslcm argumc

tuin

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P T Ó L E M AE t '' nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;»7»

-turn, Kneain directum dudam non poffe hori zontan pratter punótü atringere. Edo enim Ut ex parte altera attingat, atep fi placet ad pundu M,producatur^ in direedu E m , ufepin circuns ferentiam zodiaci in pundurn z. quonia ergo quanta eftAEinE o, tanta HE in E Merit,6^ quata B E in E D.eft autquanta H E in E z. Eiuf dem eft ergo H E in E m , Slt; H E in E z, unde E G 6c E z, æquales efte confequês eft. ImpofTibile eftergo linea H E in diredu produda,horizon tem prêter pundu T attingere.Ex his cófcquês eft, quod omnis circulus, qui alterutru hórum per medium fecat, 8ó alteru per æqualia ftcabit Hlsita conftitutis,nunc metienda eft pros portio femidiametroru æquidiftantium drculorS, qui defignati funtfupra figna circuit decliuis ad ièmidiametru circuli redi, quoufqi deprehendamus ortü coru,certo^ metiamur numero,pro ut apparet in iphatra corporea aplanae amp;nbsp;decliui. Defcribaturitacp circulus æquinodialis A B G d, circa eentru E,cuius dia* metri orthogonaliter ft ftcantes A e etD Bgt;des inde circa G reftcabimus duos arcus squales G Tet G H producêtur^pariterline^ D K H,amp; d T, Z,ea quidêratione,qua côftituimus equidiftan dû circulorû ftptaitrionalê quide fieri circa een trum E ad menfura K,auftralem uero circa idem centrum ad menfuram z.Dieoergo quod pros portio E z ad E D eadem fit, qu^ E d adE K:fiqui dem ar?

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•*® PLAN I g P M ÀB ' R ’l V M

dem arcus G h,et g T^et arcus b T, amp;nbsp;b h femicir culû æquâtundeangulos B d,amp; b d k redo æ® quales effe côfequens eft. Suntaûtanguli E D K atcß E K D redo æquales. Suntergo fimiles rcs

danguù'dùotwanguli ed K,5ôED Z. unde nei cede eft ut que Rient proportio EZ ad, D E eade fit E D ad E K. Deinde et areuû eorû,chordarûç ' proportiones afTumi'mus. Manifeftu eft enim ' quod proportio quæ eft anguU B T D,ad angu« ’ lum E z D,eam eflearcus B i* adarcû h d cum fît æquaUs B h que nimirû et arcus E z ad arcû E Dj ‘ de circulo uidelicetdefîgnato fug triangulo E D Z.undecoRquês eft,utquæfueritlinear5 E 2ad ’ E D atq? B D ad E K,eadêfîtchordp B T ad chorda' T D propordonix trianguli B T D,ct E Z D,funt fî miles. H i^ ergo habitis, metiemur in pnmis tu trunqß aremn g H amp;nbsp;g tparribus xxiq.pundts • fî. fecundis XÂ ex.eiÉ qt^e ccclxi circulum metft ’ untwr redit,qui purclb^ui; prias diximus) utrR '

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PTOLEMABh.’

*41

ufc^tropicorum diftanoæ, ab æqumoêh’ali in fphæra corporea : quod quanquâutfupra me« minimus, all) xvi.alq xviq.pundis minus inue niant, non tarnen in ortu ßgnorum magnope« re curandam gignit difcordiam. Erit ergo ie* eundum hanc diftandæ quantitatem arcus b t gradus cxiq.pundali. fecunda xx.ex eo nume« ro qui totum circulum metitur ccclx. gradib.ar cus aut B H refiduus defemicirculo gradus Ixvi. puncflavirj.fecundaxL lineaueroredla chorda arcus B T partes c pundaxxxiq.fecüdaxxviq. cxeis partibus quæcxx.totamcirculidiametrû metiuntur,quemadmodum in Almagefticon« ftitutum eft.chorda uero B h partes Ixv.puncta xxix.fecunda lyiq.Eftergo quæproportio pars tium eft centû, pundis xxxiq. fecundis xxyiq. Îld partes Ixv.punda xxix.fecunda Iviij-ea eft lis nea B Z ad lineâ E D, atcp E T ad E K hneâ. Quos niarn ergo E D femidiameter circuli recÜ abfolus te Ix partium eft, metiuntur quidem ex eis parti bus xcij. punda viq.fecundaxx. lineam E z fes midiametrum hyemalistropici,femidiametrù autê æftiui partes xxix,puncl;aiiij. fccundaxix. Ex his confequens eft,quoniam hæcièmidias metra fimul iunda, totam zodiaci diametrum faciant. Sim u lautem accepta,funtpartescxxxi. pundla xq. fecunda xxxiirj. centrum^ eius ab æquinodialicentrodiftare partibus xxvi. puns dis xxxi, fecundis Ivü]. Ponemus ergo deinde h h trunqj

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*4» nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;P L A N I S.P H AE R I V M

utruncparcuG H amp;nbsp;g T, partesxx.pundaxxx» (ècundaix. quanta eft diftantia inter æquino« clialem, 8d æquidiftantes infra punda tropica tricenis gradibus zodiaci,erit^ arcus b tgra« dus xc.pundta xxx.frcunda xix.cuius arcus chorda partes Ixvi.puncta xxiij.fecunda li. Hic ergoquæfuerit proportio partium xevifreum pundtis xxxvifrfecundislix.ad partes Ixvi.cum puneftis xxiij. frcundisli.eameft necciîe effeîis neæ E Z ad lineam e d , atep e d ad lineam E K/ undeex partibus qua lineaE d minuitur,num« rarineceffeeftin linea e z partes Ixxxvi.pundla xxix.fecûdaxlrj.in linea uero e k partes xli.pun ébixxxix.frcundaxv.HocaIiter,fî ponamus us trunq? arcû g h amp;nbsp;c T partes xi. pundta xxxix. freundalix. quanta eft diftantiainter æquino* élialcm Sô æquidiftantes infra tropica punda fexagenis partibus,arcus b t totus fucritgradu umei. punda xxxix. fecundalix. Chordadus partes xcifrpunda q.freunda xxiifrarcus uero B H gradus Ixxvirj. pundaxx-freundai. Chors da eius partes Ixxv. pundaxivq. fccundaxxig. Quæergo eft proportio partiS xcirj, cum pun# dis duobus,fecundis xüg. ad partesbexv. cura pundis xfrfr freundis xxiq. eadem eftlineæ e Z ad lineam ed , atcp E d ad lineam e K, ex ds pars tibusquælx.lineam e dcopient,lineam ezne cefleeft metiri partes Ixxîq.punda xxxix. fecun da yq. lineam uero e k partes xlviq. punda liq.

fecunda

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P T 0 L E M AE L nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;»41

fecundaxIij.Quod fi utruq^arcu G H amp;nbsp;G Tpo namus partes hir,. quanta eft diftantia ab æqut nocbaliequidiftantiu, quos tangit horizon iii climate R.hodos(quod china exêpligratia arii « mimusin fphæra corporea) erit ibidem arcus B T gradus cxliiq . chorda eins partes cxiiij. pundlavp^fecunda xxvip Arcus uero B Hgra^ dus xxxvi. cuius chorda partes xxxvij. pun* (fia tip » fee und a Iv, Sic ergo quæ eft proportio paruu cxiiq. cum punefiis vi]. fecundis xxvq. ad partes xxxvq. cûpunefiis iiq. fecundis Iv.ea dem linea E z ad lineam e d , atqj e d ad line* am E K de partibus quælx. lineam e d faciunt. habebitlinca E z partes clxxxiq.punefiaxxxix, fecunda xlfj.Exhis conftans eft,fiquidemli* neæduæ fimuliunlt;fiæ, faciunt diametrum ho rizontis , cuius modo mentionem fecimus, quern admodum diametrum zodiacifemidia metra tropicorum,earn diametron metiri par* tescnrj.punefiaix.fecundaxxx.exeis quæexx, diametron æquinocfh'alis metiuntur. undefe* midiametron horizon ris efle necefTe eft partes cii.pun(fiaiiri.fecundaxlür).centri^eiusabæ* quinocfiiah’scentro diftantiam partes Ixq.pun (fiaxxxv, fecundaiq. Hie locus eft argument! Maslem.Quia deprehenfum eft(inq'uit)quo tadiftantia æquidiftantes reefio circulo tennis nant lineam d tz,amp; d k H,utfcmidiamctros auftraliscirculi apundoT porrigatur ufque hh 1 quo

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gt;44

PLANISPHAERIVM

quo IfneaT D concurrat cum e g : uelut fi ar? cum G T ponamus gradus Ixxxix, necefle eft U nearum concurfum fieri fuper diametro cir? culi diftantis ab æquinodiali adauftrum gra^. dibus xcix. Scimus autem diftanriam poli ab æquinoÆali circulo integris xc. gradibus, quantus totus G d arcus, fi ergo in linea planis ciepolumauftralem inuenire debeamus, illic oportet,qua linea E g æquidiftans ei à pundlo D produdacontinget. Æquidiftantes uero nunquam concurrunt.ergo impoftibile eft in hanc planiciem polumauftralcm repræfenta^ ri. Nam nee fi polum auftralem pofuerimus, adefleièptentrionalem poffibilceft.Sic enim relt;ftælineæpropofitum polum tranfèuntes, e« os notant circulos, qui feie adutrunep polum interfecatSi uterq^ a defter, eas lineasin duob. locis fefeintercipcre neceftTe foret. Qtiod quoc niamin reélis lineis impoftibile eft,nee in una repr^lêntari planicieutrüq^ polu poftibile eft. Hls habitis, deinceps metiricouenit quans titatemortus fignorum,proutaccidit in fphæra corporea.Eftoenim(utfolet)circulus æquinoctialis A B G D circa centrum E, zodiac eus uero z b h d circa centrum T, diamecros rum fuper E orthogonaliter deduérarum loco meridianicirculi,alterum puncta feélionum continuât b Sé o, quæamp;fignaæquinoélialia. alterum per utrunep centrü G h Sé A z, quo^ rumpun*

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P T o L E M AE T.

rum pun Aa tropica H amp;nbsp;z » Quoniam ergo ra tiocinatio noftra demonftrandi eft, quantum in fphæra redta oriatur decirculo æquinodia« li cum quotlibctgradibus zodiaci .Horizon? tis autem rcóti in fphæra rcdta pofitio,quafi cir culi meridiani,poten tia quidem redtaru linea? rumperpolum æquinoÂialis circuli pundu uidclicetEtranièuntium, quæeftpofitio meri diani. Confiât ergo, quoniam arcus z b amp;d h funtquadrantes circulidecliuis,eosoriri cum arcubus A b amp;^ G d quadrantibus xquinodfia lisgt;cum eis^codum mediarepariter,ÓC cum eis occumbere.lincam fiquidem B D M circulo A B G D,cum per medium iècetdiametruT H,0óor thognaliter ad pundum E, æquales duos ar« eus dezodiacorefecari neceflèeft,B K uidelicet amp;: D L. producenturitaqjIineaK M, E N amp;nbsp;L C E Y. Quo fado,quoniam per punda k l amp;nbsp;Y N tranieunt circuli æquidiftantes,quorum par utrincpabæquinodiali circulo diftanria, quo? ufe^pundum k fitpotentiaoppofitum pun? do N, fic^ pundum l pundo Y, fi ponamus arcum b k fignum pifcium, erit L d fignum li? bræ.eodem modo B Y fignum arictis,ficcß D N loco uirginis. produdairaqdinea K T L, quo? niam triangulus kte æqualium eft laterum 60 angulorum cum triangulo LTE, erit 2lt; an? gulus K E T æqualis angulo LET, fic^ reliqui anguli K E B amp;nbsp;L ED, fic^his oppofiti,qui qup h h ? niam

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*4^ P L A N I S P H AE R I V M

nia apud centra æquinoâaalis circul,arcus amp;^ ciufdê circuli fub his anguK,qui cû fingulis his onuntur æquos efle neceflè eft,ex quibus unis us adcuiufc^ortum metiendum quantitatem fufficit indagari, atqj fi placet B m . Productif mus itaq^ fuper K e perpendicularem T F. quo fadto, quomam deeîs quæ Ix.diamctron æqui novbalis continent, lîneam quidemTK femû diametron zodiaci metiuntur partes Ixv, puns Äaxxxvtfecundaxvrjdinea uero ET inter eïr^

culoru centro partes quidê xxvi. puncta xxxL (ècudalvifi. Li'neaaütK Efemidiametrosgqdi ftantis circuli æqumodiali defignati ad caput pilciu amp;nbsp;caput feorpiois, puncta uidelicet A Só L, partes quidem Ixxirj. pundtaxxxixdecunda ex y ij»

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^' P T o L E M À E L * nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;»o'

ex vij. notus eft mangulus k T E. Si ergo copa* remus ad linca K E tetragonu k t , fubtracto ei tetargono T E determinabit augmentum lineæ K F fuperlineam E F. Quoties enim duorum ie inuicem fecantium circulorum maior minoré p er medium fecat, de maioris femidiametro in ieducto, fitetragonus diftantia’cenuornfubs trahatur,relinquitur tetragonus femidiametri minoris circuli. H ie ergo quonia in hunc mos dum decliuis æquinoctiakm medium fecat,fes midiameter maioris T k in fe du da maior eft tetragono, amp;nbsp;centrorum diftantiæ quantum femidiametrus minoris E B ex fdpfa producit, cum Sé redus fi t angulus BET, et linea T b æ? qualis lineæE K, lineaautcEB fcmidiamctron æquinodialis circuli,quonia partes lx. metiun tur.Exeifdemtetragonu eius iq.M D c conone reneceflèeft.dequibus inter fupradidam lines am E K metiuntur partes quidem Ixxxiq, puns da xxxix.lècunda vq. ad quam fidifferentia ils lam uidelicet tetragonum E B paremus (id eft fi quadratum E B per lineam e k diuidamus) procedet augmentum fuper lineam F E quæ funtpartes xlviq. pundalq. fecuda xliq. quod cum fixbtradum fuerit de linea K Ereliquutur partes xxiiq. punda xlviq. fecunda xxv. eus ius dimidiummetietur linea E E quæ funtpar tesxq. ex eis uidelicet quarum xxyi. cumpuns dis xxxi,fecundis lyiq,linea ET metiuntur.Ex eisitaç^

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MS, P L A N t S P A E R I V M

eis italt;$ partibus quæfîuntinlinea E c cxx. op pofitaJeiKcetredo angulo E F o, neceffeeft nu merari in tinea F T partes Iv. cu pundis ferè lix, arcum uero chordæ F E metiri gradus Iv. cum pundis xl. ex ccclxtotius circuli redanguluni triangulum E F T continentis.Ex gradibus er« go qui fuerintin quatuor redis angutis ccclx, continebitangulus FT Exxvq. cum pundis L hic autem eu angulo F e T angulo redo æqua^ tur,quiipfecumangulo B ek nibilominusrcs dumangulum complet. Subtrado ergo corns muni medio,retinquitur angulus b e K æqua« lis angulo F T E. metiuntur itaq? angulû b e K gradus xxvi). pu ndal. qui quoniâ apudeens ru æquinodiatis circuti,ôôfubiedum ei arcum B M metirineceflèeftgradusxxvïj.pundal.ex ccclx. totius circuti æquinodiatis. Hi funtitaep gradus 00 punda, prout in Iphæra corporea pofitum eft,ex gradibus æquinodiatis circuti, cum quibus üq. fîgna circunpofîta pundis æs quinodialibusin Iphæra aplanete hcorititur. Poffumus aût SCleniori modo ad hoc perueni re. Quantaenim K E in E N, tanta eb in E d . Eft aût B E in E D partes iq.M D c.quodeû diuifum fuerit per tineâ E K,coltigitur tinea E N.itaq? nos tam efle conftans eft, qua quoniam T E fripes rat duplo tineæ F E, pariter ÔC F E notam effe confequens eft, EftaûtET nota, quoniâredo angulo apud F opponitur, eritSCangulus F T

Eno«

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: rp T o L E M AB I r. T 7 nbsp;nbsp;nbsp;nbsp;nbsp;•*»

E notus angulo uidelicetK E B æqualis, quam arcus ipßus beg noticiaconfcquitur.

Q Imili modo metiri licet fequenuum ortum» O ut fi ponamus arcum decliuis circuli B K,ar cum duorum fignorum, quoufq; punctum K notet principium aquarq, pundum^ L principium fagittarii » quorum oppofita per diarnetron, n quidê caput leom's.v ucro prins cipium gemis norum.Cæte risitaqjfimili modo produ (fris, remane« buntKTÓd T Eemfdequan ritatis. Linea uero K E acs crefcat prout demonftratu eftfemidiame tron,æquidi«

ftanos circuli defignati ad principium aquarq amp;nbsp;fagitta rij, metiri partes Ixviq. punda xxxix, fecunda xlp .Si ergo differentiafupvadida, id eft iff M D C pereamlineam diuidentur,collige turaugmentu lineæKF,fuperlineamF E, quæ funtpartes xli. pundaxxxviq. fecunda xviff quodubi fubtradum fuerit ut de lineaK E,re« manebut partes xliiff punda li, fecunda xxiiff ii cuius ’

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cuius dimidium partes xxli.pundax-xvifecuft ' daxlij.lineam F E terminare confequeus eft,ex ds uidelicet partibus quarum xx vi ; cum pun« ’ élis xxxi. fecundis Ivirj. lineam e t terminant. Ex eis itaqj partibus quæ exxdineam E T, 00 re ôto angulo oppofitum Gonftituerat,entlinca F E partium ci. cum pundis xxviq. Arcus chor* dæF E,gradusxv. pundaxxviq. ex ccclx. parti bus totius circuli xquinodialis, redangulum triangulum F e T con unentes.Ex eis itacp gra« dibus qui fuerintin iiq. redis angulis ccclx.ha bebit angulus F T E gradus Ivq, punda xliifj, cuiæqualis eft angulus B e K,qui quoniaapud centru acquinodialis circuli, amp;nbsp;arcu b e a eins quan titan's effeneceffe eft. undeportione pifei umfublata, portio aquarq critreliquarum par ' num xxix. cum pundis liifj. Quam eandem efteamp;freliquorum trium, eademab æquino« dialibus pundis quantitate diftantium, id eft tauri, leonis amp;nbsp;fcorpionis fupra dataneccfli* tateconfequi. undereliquum dequadrante,id eftgradibusxc.reliquorumiiq.uidelicetgemi« norum, cancri, lagittarq èc capricomi ortus, quantitatem metiri confequens eft.

His ita firmans,intuendum eft deinceps, idem ne fitortusfignorumin ipamp;fphac# ra decliui,an alium exigat ratio quam in fphæs ra reda conftitutus eft. Sequamur itaqj mo« dum exempli dan, in Ebro Almagefti de circus lo trail

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. P T o L E M AE L »ri Ïo tranfeunteper Rhodon infuïam,cuius hori zonrispolus fepten trionails xxxvÉ gradib. a« fcendit, cuius fcmidiamcrron,ficutintcrfupra diiflaconftitutü eft, metiuntur partes etj.pun« da ürj.fecunda xlv.centric^ dus ab ^quinodia li centro diftantia partes Ixxxfj. punda xxxv. fecudaiq.Efto itacp (utmos eft) circulus æqui nodialis A b c o, circa centrum E,zodiacus ue ro z B H D circa centru T, Quo fado, inteUiga mus motum fphæræ tanquam in pundo E,1amp;:

ptentrionalipundofixo, expudo D per puns da G amp;nbsp;B in pundu a . Intelligemus itaq^pris mum dehiscirculis horizontis, duos arcus co tingentes pariter utriinqs tropicu pundum, ii * quæ

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»r* PLANISPHAERIVM

qug funt z 06 H, quorum alter z k h l,alter z M H N. Conftatitaq?cumfuerithorizontispofilt; tio ut fitus eft arcus z K H L, neceflario fimul on riri punclumZjamp;K pundum, oppofitacp his H amp;2 L,tllo momento occumbere.Cum uero ut fitus eft arcus z m h n econucrfo, id eft n 06 h puncfta fimul oriri eadem^ hora m amp;nbsp;z oc^ cumbere, dum motus fphæræi ntelligatur qua lemaffignauimus,fixofcilicet in notaE polo fcptentrionali. His conftitutis, quoniam ut fupra diclum eft,nó lolum zodiacus æquino^ (ftialem fecatcirculum, uerum 86 horizon om« nis,tamhunc quam ilium, Cumcos in hunc modum fignauerimus, necefiTe eft utlineære« cftæ punch. feÆonû continuantes K b Ô6 M n, tranftantper centrum E,ex quo con ftans eft ar cum M N æqualem efte arcui k l , ficcp arcum A M, æqualem arcui G n . Supereft ut arcus am arcui a k æqualis conftituatur. Figemus itaep fecundum hos arcus horizontis duo centra in pundlo c amp;nbsp;puncto Y, produccmus^lineas C T,86TY,Ô6ecÔ6ey.Quoniam ergo quoti« ens duo circuli lèinuicem fecanqfi lineam pun cftafeclionurncôtinuantê centra, continuans linea fecet, neceflèeft per æqualia 86 orthogona liter iècare unam 86 roftam effe linea CT Y,con icquenseft lineam zh medio 86 orthogonale ter fecantem. Hoc aliter c E perpendicularisH V,fic^ YEppendicularisM n, Sunt ergo utrin« - nbsp;nbsp;nbsp;nbsp;nbsp;« ii nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;que

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P T o L E M AB I. nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;»n

que trianguli circa e t inter C amp;nbsp;Y,tam Iatcri= bus quam angulis,pro utfefe refpiciunt,arqua Ies uidelicetangulo Y E T.funtautem amp;^ anguli Y E M amp;nbsp;c EK,utqui redi æquales. unde rendu ©s quoep angulos uidelicet a e M,atq; a e K æ# quos cHcconfcquens eft, fic^ amp;nbsp;arcus a m attp atcpA Kæquales efte manifeftum eft, fic^ L c amp;nbsp;G Njipfiep utriqjutriftp.Quoniam ergoars eus A B oritur cu arcu h b , ficep arcus b z cum arcu B K, qui eftæqualis b n, rurfusep arcus z d cum arcu k D,atcp arcus d h eu arcu d N,qui eft æqualis d k.Ex his conftatarcus decliuis circu liutæqualiterutrinqp ab æquinodialib. puns dis diftans,æquali oriri quantitate. Amplius, quonia arcus b z,decrefcitab ortu fuo fphæræ redæquantitate arcusK A, oppofitus ueroar« eus D H, tan to accrefeitquantus eft arcus D N,c# qualis uidelicet k a, æftiuus tropicus pundus Hcoftans eft,figna circa uernale tepus pquino ditr,tanto quide ab ortu fuo fphæræ rcdæ des crefcere, quanto oppofita his onû fuum fphæ rærcdæfuperant.undeconfequensefteiusclis matis minimumdiem, tan to æquinodiali die minorem, quantum conftimunt utricp arcus A K amp;nbsp;G N maximum,tantôt maiorem. HIsquoep cognitis, uidendum eft primu in hoc climate, utrû ne dierum eins difîès rentia quam expofuimus,concordctei quæin Iphæracorporeaaccidit.Defcribemus ergo hu ii , iusfigu

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‘r* PLANISPHAERIVM

fus figura, in ea^(ut ante) Horizonte per puns lt;fia z H L fingulariter. Vtergo qd‘ intendimus deprehendamus, quantitate uidelicet arcus A K,figeinus (utante)centrû horizontis in puns Ao c.producemus^ lineas e C, Sf C T perpen« diculares, lineis z h 06 K L, Quonia ergo ut eft coftitutum, lineaniC Ediftantiam centrorum

matis metiuntur partes Ixxxitj. puncfiaxxxv, lecundairj. ex partibus uidelicet,quarum line« am E T,diftantiam centrorum ^quinocHalis Si Zodiaci continent partes xxvi.puncfiaxxxi.iê« cunda Ivirj, Ex partibus ergo quarum in linea E Tjud redo angulo oppofita numeremus par tescxx»

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FT o LE MAE T nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;»er'

tes cxx. eritfn linea ET partes xxxvifj. punâa xxxiij. cuius chofdæ arcus graduïï xxxvfj. eu ■'pundis xxx,ex ccclx. gradib. itaq; ccclx. quós in quatuor rec^tis angulis numeremus, conus nebit angulus etc gradus xxxviq . punda xlv, angulus uero C e t , redum cum hoe perfi eiens,gradus Ixxi, cum pundis xv.Necefleeft ergo amp;nbsp;angulum A E k, cóftare ex gradib, wil. ^xw. xvq, pundis xlv. unde amp;nbsp;arcum A k eiufdem eHequantitatis coiequens cft. Metiuntur ergo ortuutnufq? quadratic à ucrnali æquinodio, gradus Ixxi.pundaxv. ab autumnali uero gra dusevirj. pundaxlv. undedierumlongiflimi amp;nbsp;breuiflïmi,ab æquinodiali die difFerentia graduumxxxvq .cum pundis xxx. quæfunt æquales horæduæ amp;nbsp;femis, prout in fphæra corporea efteonftitutum.

DEinceps ergo ad metiendum fignorum ortum,in hoe climate conftituemus ites rumgquinodialem circulum a B c D, circa een trum E,zodiacum H D z B.Quo fado^dezodia co refecabimus arcum B t, primum^ ad mens Furam unius fi'gni,quod efïèpifces codans eft, Continuabimus tel lineam redam, panter^ circinabimus circulum horizontis latitudine graduum xxxvi.ut anteperpunda T amp;nbsp;l tran (euntem,atcpæquinodialemad punda M 00 N fecantem,producemus^lineam m e N, fic^ad centrum horizonus ut antelocato D,ducemus lin cas

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»r«

P L A N I s P H AB R I V M

tineas refflas c e 8c E T gt;nbsp;poftremo SC perpendi« cularem lineæ t l lineam T Y, Eft ergo ut fupra dictum eft,arcus A, in ea differentia quaaries et pifces,utruncpin hoc climatedecreicit abortu iphæræ refftae, eadem^ quaoppofitorum his utrincp fuperortu fuû,infphæræ aplaneteac« crefcttConftatautem et lineam E T, femidiame trum æquidiftantis circuli defignati ad caput pilcium,partium Ixxiq.cum pundis xxxix.fe« cundis vq, ex eis quaru linea E T diftantia een* trorumcotinet partes Ixxq. pundtaxxv. fecun da iiq. Quonia ergo augmenta tctragoniTC,fu pratetragonum E T, in partibus iq.MD c.Isnu* merusfi per line am ET diuidat, profequamur^ fequentia peror dinê, qucadmo dum in fphacra re(fta,colligemus lineam E Y,ut ante partiu xq. cd puneftis xxq.ód fecundis xq. Ex partib.uci roquarum in lineaET,recdoangulooppofica numeramus cxx. habebit linea E Y partes xvi. 8ó fertpundum,cuius chords arcus graduum xyq.cum pundis xvi.ex ccclx, totius circuli tri

angulum*

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P T o L E M AE I.

»rr

ängulum E T Y cóti’nens.Exgradib.ergo quos in nij.redis angulis numeramus cedx.habebit anguIusETYgrad.vi.pundaxxxviii.exccclx» totiuscircLiligquinodialis.QuoniacrgOjUtfu pra didu cft, unumquodcß ex üq. Ognis circa pundaæquinodialiain iphæraaplanete, ont cûgradib.xxvq. pûdisl. cûdehaefummagra dus viq. cû fuis pundis fuprapofitæ fummæ adqciamus,accrefcet numerus ortusuirginis, ortus^ libræ gradus uidelicct xxxvi. punda Similiexcmplo,mctiriIicetamp;fcquê (xxviq.

rium ortu:utfî refecemusarcû b T,ad quan titatem duorû fignorû pifeiû amp;: aquarq, quos ufcp amp;nbsp;cætera modo fuperiori perficiantur, un de lineâ E T, ut potefemidiametrû æquidiftans tis circuit defignati, ad caputaquarq accrefeere necefleeft, quoufqj partes qutdêlxvi. punda xxix.fecunda xlq. cÔtineat:per quâ ubi diuilc« rimus fupradidâ differentia iq. m d c, fequen tiaep per ordinemmodo fupradidoexpleuert mus, colligemus,ut ante, lineâ c Y partiû xxq, cû pundis xxy. fecundis xlq. Ex partib. ergo quas in linea E T redo angulo oppoffta numes remus cxx.continebit linea ey partes xxxq» pûda xxxq. cuius chordæarcus gradus xxxi. pûda xxxq. ex ccclx, totius circuit' triangulû E c Y attinêtis.Exgradib.ergo quos ccclx.in iiq. redis angulis numeramus,babebit angulus E C Ygradus xy, punda xlvi. qui quoniâ eftæs

. kk qualis

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ri8 nbsp;nbsp;nbsp;nbsp;PLANISPAERIVM

quail’s anguloT em , meuentur etia arcum a m gradus xv.punda xlvi. augmenta uidelicetor tushoruduoru fignoriï fuperortumeoruin fphæra aplanete,quê ut fupra diAu eft,metiun turgraduslvfj.pundaxluq.dequafummanr« fi gradus xv.puncla xlvtfubtraxenmus,relin« queturortus pifcïumfimulamp; aquarri gradue , urn xh'.cum punctis Iviq.undeporrione pilei« urn dempta, reUnquitur ortus aquarrj in gradi

bus xxfj.punâis xlvi. Quod fî prædidæfum« mæ eofdê gradus xy.cum fuis punÆ’s adrjeia« mus, accrefeet ortus leonis lîmul amp;nbsp;uirginis graduûlxxiq, cupunÆsxxx. undeportionc uirginis dempta,relinquitur ortus leonis gras duumxxyq. cupundisduobus, Confiât au«

temtau*

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P t Ö t É M A ë f nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;if9

tetntaurumæquali'teroriri aquario, fîc^fora pionein Iconi : nam geminis èC capricorno in refiduis temporis ïpatijs, quæ Arabes Zeme« nen uocant,fui utrinq; quadrantis, quoniam Só cancer amp;nbsp;fagittarius in fui utrinqj quadrans ris temporis fpatqs refiduis oriuntur.Gemino rum quidem amp;f capricorni gradus xxix.Cani cri uero amp;nbsp;fagittarg gradus xxv puncta xv.ex ccclx.æqualis circuli gradibus, in quarto uide* licet climate Rhodi infulæ, quod medium bas bitabilium exempli caufa affumimus in fphæs ra: cæteris ad imitationem eius ad eundem mo dum contrahendis,

PLANISPHAERII PARS

s B C V D A.

V P E R i o R i S tradatus parttcula 0 de circulis æquidiftanribus recio, ufcpadfignorûortii continet. Hu« ^ ius habet æquidiftantes zodiaco, quouii^affîgnent locaftellarum fixarû,quara rioneeas contineat,idquodin horofcopio ins ftrumento aranea uocatur. AiTumimus ergo ëx deicriptis circulis eum qui extrinfecus ambi en s, omnesalios intra feconrinet,eum^defcri bimus nous A B G D circa centrum E,cum circa lis meridianis,cuius diametri ieinuicem ortho gonaliter fccantes a G amp;nbsp;b D. quo fadro refecas mus ex pundo d arcû d z,cuius quanutas ter« kk * minetur

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»«® P L A N I s P H AE R I V M

minetur ad menfuramdiftanriæ,à circulo gqui noStiali scquidiftands ei,defcripn ex partepoU auftralis infphgracorporea,producimus dein deUneam à pundlo G, æquidiftantem lineæE T,terminatam noris G H,defcendet^ panter ex punâ:o H,fuper lineam e d perpendiculans H T, applicabis amp;nbsp;G cum D tranfiens h t kneam ad punctum K. Dico ergo quod fi deknea a e refcindamus æquumT K, idc^ad punctum L, defcribamus^ circa E centrum,ad menfurara

E L circulum c L M,critdiftanria a B G d à circa lo c L M defignata, ad quanritatem arcus fimi* lis arcui D z,quod ut plane confict, applicabis G eu M, fecans circulum c L M ad punctum N, erit^arcus M N,fimik’sarcui d z,fic^arcus G Z, reliquusdequadrantefuicirculi fimilis arcui L N,rdîduo dequadrante circuit fui:quod ita plane

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*lt;sr

plane fumi poteft. Eft enim quanta d e ad Ii« neam E G,tanta d T ad lineam E K. Eft autem D Eæqualis c e,eft ergo amp;nbsp;d T æquahs T K. atues ro T K,cqualis t w.Eft ergo E m æqualis T D.acs cepta ergo T m in communi, erit E T æquali's M D,extititautêæquah's equidem amp;nbsp;G H. ficergo Só M D, æquidiftans eftjæqualis 8c eidem G H, undeamp; H Datlt;^G M,8ôæquales amp;nbsp;æquidiftan tes eflè necefte eft. Eft ergo angulus G m E,cqua lis anpulo z D E. unde arcû c l N. arcin' l b z ft mile elle confequéseft. ficcpamp;refiduûrefiduo defemi'circulis, id eft M NjCi qui eft z D,fimikm efte cÔfèquen s eft.Si' ergo drculus c L w, ftatua tur æquinodialis, erit ci'rculus ABC D,dcfigna tus ab eo ad diftantiam arcus l n , arcui G z

firn il s»

DEinceps conuenit propofitum infèqui, defignandi uidelicet circulos, quoru ha« bitudo ad sodiacum,quail’s co rum qui deferi« pti fun t ad æquinoÂialem, quoufep pateat n 0« bis pofitio ftcl!arü,habitudmecarum ad hunc circulum,præter eamquæad æquinocftialem, Efto enim primo loco circulus æquinodia lis, decirculis planifphacrrj defcripris notis A b c D,circa centrum E^zodiacus uero l b H d cir* ca centrum K, lincarcdta per utrunep centrum tranfiens L A H G, fcCtioncs uero circuloru con tinuans linea bed. rcfccamus itacp arcum b T ad quantitatcmarcusdiftantig,interpolumxs kk , quino«

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»«» Ï» L A M I s t» H AB R 1 V M

Äialis Circuli amp;nbsp;polum zodiaci, tranfibit amp;f h* nea per d k T,pundum uero K,pot€ntia refpici ens polum zodiad. Confiât ergo,quod fi hæc diftanria ftJtuto terminetur computo,drculus ab hoc pundo per gemina zodiaci punda per diametrum oppofica tranfiens,fecet amp;nbsp;gquino élialem circulum per medium. Conftat enim drculum omnë,qui alterutrum horum per dia metrum fecucrit, amp;nbsp;alterum per diametrum ié«

«are,crit^ drculus bic magnus,ambiêsutrinq^ orthogonaliter interdpiês, Hic fubiugit Maß lern, quod cum huiufmodi circulus mplahß fphærio defcribatur,fî per gradum fteUæ trän:« feat, ütrunque fi ta fît, tranfirequoqj hune per ipfumeorpus fteUse. amp;nbsp;fî per ipfum corpus ftd Lctran

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P T o L E M AE I» nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;ut

læ tranfeat, tranfibit eaam pergradum ftellæ. Ampliusji'neae rcdæ percentrum æqumodia lis circuli în planifphærio tranfeuntes , fuper corpus ftelîæ tranfeant, tranfibuntôc per gras dum, quo cum ccelum médiat, id eft,cum quo ipfa tranfibit meridianâ hneâ. CÔuerfo quocp, fl per hune gradum tranfeant, tranfibunt amp;nbsp;peripfum corpus ftellæ,ubicun(^ fîta fuerit. lt;nbsp;NV ne æquidiftantium zodiaco in planis fphærio deferiptio notanda, Deferibas

musitatpdreuïummeridianû per utrueppo« Ium tranfeuntê A B G D drea centrum E, axern inteUigibilem lineam D E B,punélum d auftras lem polum, intelligentes diametrum circuli æ# quidis

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»«4 P L A N I ff P H AE R I V M

quidiftâtiszodiaco c HT, quêinpiani'fphærio deferibere propofitû fît.Deducimus itaqjper pundtum Hjincam æquidiftantemlineæ a g, notis K L,terminante tineas D w z, amp;nbsp;d c L,atc^ D N T,continuantes.Dico ergo circulum cuius diametrus ZT,dcfignari poflè circa diametrii M N. côtinget enim hinc inde duos circulos æ« quidiftantes æquinocTâali: quorum ab eodis ftantia inquantitate arcuû a z Slt; G T,fecabit8^ circulumæquidiftantêæquinodliali, cuius dia metrus L K, per medium apud circulum men's dianum,cuius diameter B D, quem ad quantis tatem c e, deferibimus internotas C Y F,quam per medium fecabit circulus circa m n , deferis ptus per puncta F Ytrâfiens. Applicabûtitaep lineæ redæB cumz,amp; Beum Ct^procedunt 06 K L atcp D T in diredu, quoufq; concurrant adpundum K, Quoniam ergoanguli duo d Z B3amp;B H etreeftifunt,confequens eft B h QZ puncta per circunferentiam circuit locata, uns deangulum B QH, æqualem eflè necefleeft an gulo B Z H,qui æqualis eft angulo B d T, quoru eaedem bafes.fic ergo angulus B Q.K,gquaIis eft angulo B D K. unde pundta B d K ctfuper cirs cunferentia circuit eftè locata conftans eft, Eft ergo,quanta b h in Y D, tan turn K h,in H Q,dus da. quan tu uero b h in h d , tantum quod h b in fetpfum producit. Eftergo quantum h Lin feipfumduda, tan turn K h in h Q.,^quidtftans lineæ

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fineæ M N. Eft ergo quanta E M in E N, tanta E c in feipfam duda. Quæ quomam æqualis E Y, êc E F punda N Y m F,fuper drcunferéntiacir« euhlocatacffeconfequenseft. Maslem addit, dreulo æqui’diftantezodiaco(cuius diftantia Ïaritudinê ftellæ metitùr ) firmato, deducemus àpolozodiaci in (upradatadeferiptione, notas to arcum per gradum ftellæi n zodiaco,tam zo diacum quàm æquinodialem per medium fes canris dreuli. Vbi ergo is arcus gquidiftantem Zodiaco (ecuerit, is pundus eft ftellæ locus in planilphærio. Hac conftituuone de æquidis

ftantib.zodiaco habita,fimili ration e, h fdem^ argumenos côftitui poHu nt, 8ó æquidiftantes horizonti,quos Arabes Pontes nominât,quo rumuerticales circuli, id eft paralleli dudi, ex Uerticecapitum, tanqua centro funthorizon« d, ut æquidiftantes dreulo redo.

tl Circule#

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*^^ PLANISPHAERIVM

Clrculorum æquidiftanrium zodiaco inlt; hune modum defignatorum,diuerfafem per efle centra neceffe eft. Sit enim(ut ante)drss culus meridianus A B c d circa centru E,axis lis

nea bed, diameter circuli æquinodialis linea A G, diameter circulorum æquidiftantium zo« diaco lineæ z h amp;nbsp;T K,producentur ÔC lineæ D L z,D M H,D N T, D c K.defignamus deindecirs ca triangulu d n c circulum d Y e , produda Y, F, deinde diuidemus lineam l m per medium^

apud punctum


ftansfitcirculos circa diametros ZH, deicribipof efe circa dia mes truLM, ficepcirs

. culum eins circa

diametrum T K, Dico hos duos

circulos nequa'

quam effeeiufdemcentrijid eft pundum o in diametro A c,minime medium eflè. Qiio«

niam enim arcus z t æqualis arcui K H,erit ars cus Y N gqualis arcui c F,undelineæ l m amp;nbsp;F Y acquidiftantes. Ergo quæproportio lineæ D L, ad B Y,eadem lineæ D m ad m F.at uero que pro porno linee d b,ad lincâ l Y,ead€ linegin ft du (ftæad DE in vYduCta^Eadem^lineg D M in ft dudæ

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P T o L E M AE I» nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;i«7

dudkcad D m in m F duda, que dm ad d F linea proportio. Quoniaitaqj loco circuli D t, in L Y equalised LT, in l M,ficcp l D,in m F,æqualis MN incM,erit^proportioclinfeduclacad c L in L NjCadeiu^ linea in feipiam ad m n in C M alternatim. ergo quæ proportio tetragoni D bad tetragonû d m , cade fuperficici c l ex L N produdæad fuperficiéex N m amp;nbsp;c m côftitutâ. Eft aût tctragonus D m , maior tetragono D b, pro ut D M longior^ D b. fie ergo N m in c m ma ior, ^ c b in b N. Cum ergo cômune mediû N c, mains fîtefi m c in m c, quàm cû b n in N b, maioréefTe c m quàm b N coftans eft. Data ue# ro eft M o gqualis b 0,minoré ergo eflè 0 c quâ 0 N cofeques ed.Nucergo punctû in 0 diame tro NC medium eflèpofTibile eft: qd‘cum me# dium fit in diametro M b, circulorugquidiftan tium zodiaco,idem cflecentrûimpoflîbileeft. DEinceps quoniâ æquidiftans zodiaco, nec in planifphærio deferiptus, nec in (phæra defignatus,cuius portio in parte appas rente, fecatæquidiftan tes circulo rcdto,non ap parentes penes polum auftralcm : quorum dis ftantia à zodiaco aut à capite cancri minus alri tudineeius in loco definito, aut àcapitecaprin corni minus eius altitudincinloco détermina to. Ponemus circulû meridianû a B G D circa centrum E. inteUigemus itatppuncrum d pos lum auftralem, axem ucro b D,diametru circus 11 * hæqui

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*«« P L A N I S P H AB R I V M

UæquinodlialiSjA g diametrumdrcuù'æquidi diftanris et nunquam apparentisjtneamz H diametrum circuit hune fecantis,ab æquidt'« ftantibus zodiaco,lineam T K uQuibus itapo fius,de(îgnamusfuperlineâ z H feintcirculum Z M, erigimusep lineam à pundo K in M,acquit diftantem E d . Ex quo itaque produximus lineas a G n,8c D H N atcÿ D l c,eritcirculus qui defcribaturad quantitatem E N,inter notas N Y Q^decirculis planifphgrio perpetuo negatis»


Circulus uero qui deferibatur uicedrculi,qui fuper lineâ T K L tran fire neceffe habet, per pun dum E,circulum N Y Q,fccans in arcus fîmiles arcubus h m amp;m z,cum fitlineaK w commue

ne medium fuperfidebus eoru. Applicetigitur F cum M, eat^adpundum E,fuper lineam e a angulus æqualis ahgulo M F K,undelinea pro« duda

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P T O L B M AE h nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;*«*

ducflafn punctum Yproucnicns,arcumY qQ milan arcui M z demonftret. Eftoitaep circus lus defignatus uicecirculi, quifuper lineamT K Læquidiftanszodiaco,cuius diftantiaab æs quinodiali in quantitate arcus c l, perpetuo laten tes circulos relt;fto equidiftantes, huiufmo di fimilitudinemlècans hiccirculo,tanquain defcriptione figuræ appofito inteUigendu eft, utper camp;Y tranfiens in oppofito pundoo deprehendat, qua D T amp;nbsp;T A in dircÊtum pro« dudæcocurruntjearatione quaD h Sc e g ad punctum N conducit. Deinde argumentum quod Maslem fubiungit addes, producimus lineam d z in diredu, quo ad puntftum Q.nes ceiTario perueniat, quemadmodum amp;nbsp;d h in punduniN peruenit, utquemadmodum fus pradicdis defcriptionibuscoftat. Sitcirculus, cuius diameter z h circa lineam qn defcribis tur:ficutcirculus cuius diameter T k L,dcfcnbi poflit circa linea o C. placet itaq? D cum K,eat^ in diredum ufepad pundum K. fieep e h in dis redum ufq? ad pundum p , procédât à puns do T in pundum xjinea æquidiftans lineæ H P.diuifa ergolinea c N D,ad fimilimdinêpros poraonis partium ^quidiftanns Gbi h p, quos niam angulus d T z, æqualis eftangulo d l t, angulus uero d T z æqualis angulo D T H, erit angulus D T L,æqualis angulo d p H.Suntitalt;^ punda L s T P,fuper diametrum circuli locata.

11 i unde

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”'® P L A N I S P H AE R I V M

linde quanta s b in K P du da, tanta T k in K L. Exiftitautê quanta KT in K l, tan ta KZ inKH. æqualis ergo k z, in K H duda, quod K s ex K P producit. undead eundem modum, quanta K in KN, tanta in o RinYC.AppIicetitacpKcum z,erit^ F angulus k ei fimilis KFM, cum 5lt; an« gulus apud F, æqualis fitangulo apud e , amp;nbsp;li« neæeos angulos continentes,proportionales erunt. EruntergoSó rcliquieorum anguliæ« qualesîutcû redus fit angulus K m F, Só angu« lus E K Y, reduelTecofequens eft. cqnalis ergo Q.K in K Q,, lineæH z in leipfa dudæ, quæcum perpendicularis fitlineæEo,puncta Yc o fu« percircunferentiâcirculieiTeconfequêscft.Ex hispala fit, quod infphæra dum lupcridem centrum æquidiftans rcdû,amp;æquidîftans zo diaco,mcdius medium fecat : quod quoniam planities ferre non potcft, defcriptione, quam Maslem ad iddemonftranduhicinterponit, fuperfedemus,nequidpræterPtolomaicæde« fcriptionis inten turn, ut minus cauemus plus apponamus, præfertim eu nullaneceflitas co« gat : quod tarnen in ipfis defcriptionibus eius qua locus cxigit,imitatione Maslem no negli« gimus. Necenim defperetquifquä,quin nos quoq?, 8lt;Sea quæ Maslem interpolait,etiam ex nobis ipfis quàmplurima equèrationabiliter, utilli uifum eft, inferere poflemus, nifi autoré ipfum ut decetcaftigatè fequi mallemus,ucriti, neimmo«

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P T o L E M AE b

in

neimmoderataeuagandi Iibcrias, nimiæbene uo lent uv uitium incurreret.

Similis deferiptionis cxêplo,nihilo minus concipi po reit amp;nbsp;drculus xquidiftanszo diaco, qui fupra diametru D B ufeç ad pundu C cducitur, deinde à pudo ejinea c B perpens dicularêlinca A c N,qu^Iineæ m planifphærio loeti obtinetcirculi, cuius diameter D L, eu om nes redæ lineæ à puncto D E dude, nice horû cireuloru in eadem fint planitie, quæplanicies eft circuli:cuius planiciei atcpplanick circuli ^s

quinodialis comune medium linea H c Y,pla« nines quoep circuit mendiani, quæfuper linea F D eadem ,amp; fuper utranqjillarum planicieru orthogonaliter.AdditMaskmjquan tumble lineareda circulum latentem in arcus fimiles arcubus, quos refeindit in fphæra corporca.

Quod

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gt;74 PLANISPHAERIVM

Quod ut planius conftetZefto diameter ciraiK acquidiftands retfüo perpetuo latend linea Z P K H, eritcp circulus defcriptus ad diftandam A Z,de perpetuo latendbus. Fietitacpfuperli’ne« am z H femicirculus,eat^ à pundlo K linea K m, æquidiftanslineæ e D.Quemadmodumitaep circulus æquidiftans zodiaco defignatus fus perdiametrum D L,fecetin (phæracirculumla tenté adpunétû N,in arcubus H m Ôf m z,Gcli nea B Y.circulû enim Y Q.in arcus N Y, et Y Qar cub. B M,8d M z fimilesî cuius argumento appli cabit c eu Y, amp;r F cum M. Quoniâ itaqj linea F M æquidiftâs eft lincæ N E.erit^ propordo N E ad E C,qug F H ad F K, fed N Eæqualis e Y. ficep F H equalis F w.Qug ucro propordo E Yad E c cadéM F ad K F, atqjangulus Y c E redus, Gc^ angulus M K F. Gmilis editaqnriangulus M F K triangulo Y e c.Gc ergo amp;nbsp;angulus Y E c æqua lis eft angulo M F K,undearcum N YarcuiB N. Geep reliquû reliquo defemicirculis Gmiles efte confèquens eft.Secatitaeplinea B Y circulû N Y Qjinarcus Gmiles arcub.quos circulus æquidi ftans zodiaco,decirculolatenterefecat in fphg ra corporea.Cum ergo circulus perpolum las tentem tranfeatin ea planicie, polus illeincidit M,cuius partem cum planicies poliapparends incidat minime, cumufqj ad polum peruenit iUum.GclineaBYlicetin inGnitum protrahas tur,nunquam fecum concurret,Ex bis manife ft uni eft

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P T o L E M AE L

ftum cft j quod confèquens eft, eu lue circulus æqindiftanszodiacoj pcrpolumcirculi traniï ens ,hic æquidiftantem redo medium fccepöó hune per polum zodiaci neceflario tranfire.

HAc itaq? rauone,conuem’tinplanifphac rio fieri conftiturionêeorû,quæin fphæs ra corporea circuloru : quorum inuenrio cau^ (à circuli cquinodialis,qui' eorum æquidiftan tes ei,qui SC circuli meridiani. Circuloru quo« queinuentio,qui caufa zodiaci, amp;nbsp;qui eorum æquidiftantes ei, qui Slt; horizontis, cum quis dem inhuius conftrudionc,polus æquino« dialis circuli centri locu obtinet,amp; ipfi circulo redo,amp; cundis redo æquidiftan tibus. Quæ ratiOjCogit feptentrionales femper efte minos res,auftrales maiores: illos quide decrefcendo, ut in fpliærajios uero crefcendo, ueria uice atepin fphæra,paritcr meridian os omnes in re dumextendens.PoIus autem zodiaci, neepip fi centrum eft, neqp ulli æquidiftantiû ei. Quis bus euenit, id^ unus cord fine eentro eft,amp;f lis neafitredadn circulus uero magnis per hune polum tranfeuntib.aliter,tranfeuntes quidem perpolum utrunep redæ fiunt lineæ, in quis bus centra æquidiftantium zodiaco,locamur minime equalim Vndein aftignationibus ftel larum,utrumlibetfiatprimahabitudincadcir culum æquinodialem, fiue habitudine ad zos diacum, in utracp amp;nbsp;zodiacum amp;nbsp;fquinodia m m lem dis

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»74 FLANISPHAERIVM

lern diui'dimus. Sed fi fuerit habitudinc ad æquinoctialem, diuidcmus cum ipfo pari« tergquidiftantesei. Si uero habitudineadzo« diacum,cum ipfo amp;nbsp;gquidiftan tes ei. Vtrumk' betitaq^fiat, pofitionê ftellarum affignatcerrif fimam, inter hoc ut utroep modo adæquetur ri quodfitin fphæracorporcatdeterminatis ut delicet ris, quorum inuendo propter circulum æquinotfh'alem.Hi qui ad sodiacum adhiben tur,ad exemplum fiant quanta fieri poteftpro pinquum Ægypto.Necefi necefle omnia in planifphærio exequigt;obferuaris circulis tranie undbus gradus binosuclternos,uel amp;nbsp;fenos in mediocri : qui numeri communes,trigenis uidelicet fignorum gradibus ,qui inter æqui* noâ:ialem,ô^ inter utrunep punclu tropicum, quo ufep incidant cum ipfis circulis tropi

cis, 8ó cum circulis meridianis, figna diftinguens tibus,

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lÖRDÄNVS


*7f


DE PLANISPHAERH FIGV«

RATIONS.

P H AB R A M in plano defcriberejed fînguîa puncta dus ni piano quoli bet ordinäre, fecundum fimilitudf« nem finis : in quo confpidens alter

poloru,uidebit fphærâ contingente planum in reliquo polo. Imaginaniur enim, qd* plana fuperficies fphæramin alteropolorû fuoruni contingat. Reliquum polum,uirtutem puta« mus habereuifiuam. Partes autê fphærc,non poffe radium terminare,fed ipfum ufq? ad plas num(quod propofitum eft fphæram contins gere)deferri, 8ôab eo often di,ibi^ quodlibet punctum fphærg uideri, ubi radius à polo ui« dente,per pundeum ipfum tranfitus planum contigerit, amp;nbsp;ad ipfum incident. Erit^plana “ fuperficies hæc,ex radiorum à polo uenientts um,occurfu fecundum fimilitudinem fphgra um pundorum diftineda: illudq planifphæri ' um fine aftrolabium nominamus, Quippe, ■ quæcunq^ pafliones uariationem fitus puns ' dtorum in fphæra(qualis ex perpetuo motu es ' is accidit)mutuo fecomitanturteadem fimplis citer uariationéfitus eonmdem, in piano mos ’ do reprefentatorum confequuntur. Oportet autem fuperficiêhanc,indefinitæ quantitatis mm 1 intdliges

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276 nbsp;nbsp;nbsp;nbsp;PLANISPAERIVM

’ intelUgcre, coquodfitomniüpunctorû,quiin fuperficiefphærgfunt,polo,cui uifiua uinusat tribui'tur duntaxat excepta, reccpdua.Poflibi« leenim eft, utqudibetpuncdus fphær£,in cons caua fuperficie fignatus, omnia puncta eiufdê cauæfuperfidei uifibilîterapprehendat, feexce pto. Id^ de punctis conuexæ fuperficfei,obie« élu foliditaris fphærg circunfcriptis, intelligen dum efLQuihbet enirn punétus, etiam in con uexa fuperficie fignatus, omnia puncda in cas dem fuperficie uifu percipiet,fi fphgrg foliditas non refiftaLQuia uero in piano folam fphær^ fuperficiem reprefentamus, nihil deipfius pro funditate animaduertimus. Nam quæ paifios nés fequuntur motû fphxrc, omnes amp;nbsp;eadem fequentur motum, uel folius fuperficiei ipfius, utpote,fi opinemur inanem. Hanc uero fus perficiem, intellexeroindiffêrentcreiTe conca* uam eius uel conuexam : nihil enim horum us trumlibetdiffèrt. Etquia in fuperficie tantum punéla ôé lineæ diftinguuntur, aut partial les fuperficies,quæ mediantibus lineis ex toto fèparantur.Idcirco in opereplanifphærrj,folas lineas neceiTeeftprotrahere, aut puncta figere. Atueroomnis linea,quæinratiocinationêad duci potefi, in fuperheie fphærg protraélaeft, autcircunferenria,autarcus. Nullamenimre« edam lineam fphærg fuperficies recipit. Ergo omnis lineaquamin afirolabioprotrahimus,

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I o R D A N I.

«77 circunférentiam alicui drculi fphærg, au tare 5 ipß us in plano repræfentat. Primo igitur dos cet,fub qua figura quilibetcirculus, qui eftin fphærajn piano reprgfentetur, quia uclpcrcir culum,uel per lineâ redam. Attende autem dis ligenter, quod nulluscirculus,quêlinea reda reprgièntatin piano, poteft totus reprgfentari. Namomnes tales, fiuefintdemaiorib. fiuede minimis, per polum,cui ut uideat tributueft, tranfeunttitaepnon caduntomnia pundaeos rum in pianum. Polus enim coru, rit extra pla num.Sed nee omnia etiam prgter polum :nam ubi iftud, fieret Iineainfinita.Cundi autcircus li fphærg, qui percirculos in plano defignâtur, ex toto pofluntreprefentariin plano.Secundo docet, qualiter omnis circuli, quorü in co paras tionead redurn funt fitusnou ex redo,aut qua liter redusex fingulis eorü eliciatur.Etqd'quis fplam eorü ex akero non elicitur,etia cognito fi tu,no medianteredo. Vocataut redurn cireu lum maioré, cuiuspoli funtpoIifphgrg.Hunc aüt,in codefti iphærauocamus equatorê. Per hune itaepfeimus omnes circulos,quorü deeli natioes à redo funt notæ,fiuedemaiorib. fint, fiuedeminorib.in plano dcpingeretutgquatoi rem, tropicos, figniferü, Horizontes, meridias nos,circulos altitudinu,difcretores horarü,do morum, amp;S plures his,itaut uolucrimus,amp;u ti* le iudicabimus, Tertio docet omnia puncra mm , iphære

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*78 PLANISPHAERIVM

fphære,quorum à nous pundis orbis rcdti no ta eft latitudojin plano figere.Per hoc ergo,feie mus polos omnium circulorumin planolo« care, fed amp;nbsp;ftellas fixas in rete difponere, co^ gnito gradu,quo cum fîngulæ mediant coe« Ium. Quarto, docet quemlibet circulum maio rem,per partes æquales uel notæproportionis diuidere. Per hoc quocp feiemus orbem figno rum in dodecatamoria, amp;nbsp;hge in fuos gradus partiri. Horizontem quoqî,amp;quæcuncj5 no« tæquantitatis,in partes ut uoluerimus,diuide re, 8lt;^exunoquocpquantam uolucrimus pars temrefecare. Quinto amp;poftremo loco,docet omne punAum, cuius in fphæra à nous puns eftis orbis decliuis notaeftlatitudo,in plano lo care. Per quodfeiemus omnes ftellas fixas in reti ordinäre, cognitis locis earum in orbe fis gnorum, amp;latitudinibus ab eo. Scireautedes bes, quodomnis fuperfi'ciescontenta,aqualis betlineacircular! in planorepræfèntatcuruam fuperficiem, conten tam ab ea quæ per ipfam re præftntauirinfphæra. Excplicaufa. Circulus capricorni, in plano reprgfentat curuam fuper ficiê fphæræ, qua feparat ex fphera tropicus ca pricorni, polü arétied uerfus.Et hanefimilitus dinê intelligein cætcris.Hactcnus Protheoria, SPhæra inuno polorum planu contingent te, in cuius fuperficiefitcirculus,perutruc^ polumtranfiens, fi quotlibet lincæàfuperiori polo

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I o R D A N I.

tT9 polo ad circunferentiam ilhus circuh’ defcens dant in planum,puncla in quibus planu cons tinguntjin rccia linea fitaerunt, Qiiod fi idem circulus per polos non tranfierit, in circuli cirs cunferêtia fita crût. Alia lectio fie. Quod fi ifte circulus per polum, ilium oppofitû polo cons tingenti planum, non co tin gerit, in circulicirs cunfercnriadifponcnturfupcrpunAa,in quis bus lineæ plan urn contingunt.SitpoIus plas num contingens b, amp;nbsp;oppofitus (uidelicctfus perior)fi t a,circuluscp per bos tranfien s, fit a h B K, amp;nbsp;linea G b d fit communis fedio fuperfis ciei huius circuli amp;1 plani, quæ ipfum planum amp;nbsp;fphæram continget. Dico ergo quod ipfa If nea g b d eundem circuit! a h B K habet in plas no repræfentare.Omnis enim linea reda ab a, per circunferentiam eius ad planum tranfiens, in ilia linea terminabiur.Sola autem linea cons ringens fphæram in a,quia eft gquidiftans ipfi G B D, non contingctplanum.Ideo pundum Afolum,defphæranon poteft rep raden tari in plano:fèdomnisaliuspoterit,cbquodlineaab A ad ipfum d uda amp;nbsp;ultra protrada, potcrit cos Uenirecum piano. Etpundus,in quo dida lis neaplanum terigerit,geretuiccm illius pundi, dico, per quern in fphæra tran finit. Sim iliter os mm's circulus per A amp;nbsp;B tranfiens, in plan o res prafentabimr per lineam redam. ft ipfa erit comunis differentia plani amp;nbsp;fuperfiäei,in qua iUcctrs

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as® P L A N, I s P H AB R I V M

ilk circulus eft defcriptus. Ex eo mani'feftu eft, quod perdiametrosaftrolabij repræfenuntur coluri, SC fimiliter omnes circuli tranfeuntes per polos, repr^knta ri per Itneam diames trakm debent in plaa no. Item fttalius cir« cuius,qui non trank at per a b polos, file er go aut erit redus, SC hie eft quern æquino dialem uocamus:cu ius diameter fit c b,. aut aliquis æquidis ftantium redo, quo« rumunus,cuius dia« meter fit H p.Et eft de omnib , his ratio de* kriptionis eadê,quQ adintentionê prüfen tem.Ex quo .n. circa polos A amp;nbsp;B in fphx lt;nbsp;rafuntdefcripti, eer« tum eft, quia etiam in plano per circulos æ« quidiftantes habent defignari circa pun«

dum B, aut crit circulus ille nec^ redüs,necç re« do æquidiftans,aut erit tune unus de maxi« mis,aut

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IORDAN!»


gt;ti


mis, autaliquis minoribus, Sit ergo primum unus demaximis,cuius diameter h k, eritergo E centra cÔmune ipfîôf alq circulo per polos tran(èuna,qui eft A H B K,eus lus diameter A B.Igiturducâ tur lineæAKN amp;S A H M. Cu l'giturH AKan gulusperxxx, ^ tertij Êuclidis fît reCtus, fè« quit per vifî.iè xti) eiufdem^ linea a b erit proportional lis interim B,et B N. Eadetn neceffî täte erit ipia A B pro« portionalisin ter portiones MBÔCBNter« minatiuas li« terarum,quibus aliædiametri illius circuli defî gnantur in piano,fîcut in præfenti defignatio« neH K,diameterreprgièntaturper lineamM N» Quia igitur omnes lineæreprælèntatiuædia«

n n métros

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■ïS‘ PLA N I S P H AE R I V M

trorum diAi circuli,fecantfe in puiiclo B,amp; in ter earn feÆones eft proportional!tas tranfiti« ue fumpta : manifeftum eft,quodipfæomnes circulo infcriptibiles erunt, amp;nbsp;ipfe circulus no fuper punctum B,fed fuper punctum aliud des fcribiturin plano.Et per hocpatet ratio delen ptionis figniferi,quantum ad hoc,quod fuper centro aftrolabq non potuit defignariJtem fît unus deminoribus no æquidiftantibus gquis nocftialijCuius diameter h k , 8ó fîtpoftea unus æquidiftantium recto,cuius diameter fitz c,lè cans illum quocunq? modo:quorum commu nis differentiafigneturlinea LP V, quæperfus perficiem circuli A z b k per polos euntis ortho gonalitertranfibit,8ó equaliterhinc inde,crit^ V P equalis l P.itat^protrahanturlineae a k n, A H M, ÓÓK b , exeattç linea z c ufe^in F.Item ex pundloTjducatur TQ.acquidiftans ipfi lev, Óó earn in plano reprælèntans,dult;ffis a l T, A p R, ÔC A v Q., Cum igitur anguli, A k b 8ó F Y A fintrecfti,etangulus F A Y,fitcommunis utriep triangulo, erit angulus A F Y angulo K b A æs qualis. fed angulus K b A perxx. tertq eft æqua lisangulo k h a: igitur erunt duo trianguli fîs miles,fcilicet K F P, 8ó o H P. Pofito o in fedios ne A H,ÓÓ Y P.Brgo ficutK P,ad o P,ita F P,ad P H. Quare quodcontineturfub K P,amp; P h æqua tur ei quod cotinetur fub F P, amp;nbsp;p o, fed quod fub K P amp;nbsp;P H continetur,eft gqualelquia in eos demcirs

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IORDAN!» nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;as,

dem circulo fe fecant, ei quod fub L P, amp;r p v^ quod ergo cotinetur fub N R,8C æquatur ei qd* fub T R amp;nbsp;R Q.,propter æquidiftanriû linearû. Ergo circunferentiacirculi cuius diameter eft K H,fi in plano debet repræfèntari,tranfibit per punda M T N Q.. Et hoc eft quod uoluimus demonftrare » Per hoc intelligitur qua ratios ne in aftrolabio,horizon amp;nbsp;illi æquidiftantes ducantur, Circuli omnis,cuius in fphcraportio eft no ta,eius S^ in piano defcriptio erit nota,has

bito redo, Redus quidem hie eft, uel per ft fts cundum quamlibetquantitatem formaris,uel per quemlibet fuorum gquidiftantiu. Primo itac^ipft ponaturin piano,defignatusnotis A B G D circa centrum E,dudis diametris a c b D» n n * Si igitur

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PLANISPHAERIVM


Si igitur d aliquem æquidiftantem' collocare uoluerimus , cum conftet idem habere een« trum,amp;: latitudinem eius à reCto in fphæra fcia mus,huic arcum æqualem fumemu s ab aliquo horum quatuor punctorum, amp;nbsp;fit g h contra D,ducemus lineamo h K.Si igitur fuerit circus Iusille,qui repræfentari debet in plano,fupra centrum fcilicet, polum fuperiorem uerfus, res preien tabitur circulo x K, circundudto fecuns dum diftannam E K.Si uero fueritfub rc(fto,fu meturarcus lantudinis c l , contra b, amp;nbsp;duda

linea d t L,formabis tur circulus fecundu diftannam E T, Sit es nim, ut folet,iuper po los tranfiens circulus AB, linea eum in plas no contingens B v.Et fi t diameter redli circu li R o Y, amp;ei æquidis tantium diametri QS c,8ó P N x, pertranfes at^ linea A c F v, pros trada R o Y ad F,iterS trahatur A Y zSC AX M.SCASNOB.Quia igitur o Y eftæqualis . o A, erit amp;nbsp;B z pqualis BA:cumlt;^ ficBZ,cEs qualis

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quail’s E G,cx hypothefi erit B Aæquahs E o, quiaeriamarcus h G c l fumpti, crant fimiles arcubus c Y amp;nbsp;Y x.Erunt 00 too arcus B L, b h fimiles arcub. B x b c, amp;nbsp;anguli qui caduntin eos æquales, qui funt ad A amp;nbsp;d . Igitur fimiles funt trianguli ß a v,e d K, amp;nbsp;trianguli B a Mjamp;f E D T, Cum fi t ergo b a æqualis c D, erunt amp;nbsp;b M, 80 B væquales ipfis E T amp;nbsp;C K.ipiî ergo funt femidiametri circulorum æquidiftantium res c7û in piano pofitomm. Adhuc trianguli b a M J b A v lun t fimiles triangulis E d T, e d K.Itacp ponanturnotæubi c Dfecatalioscirculos,exs empli caulà F amp;nbsp;z, amp;nbsp;ubi d t interiorem fecat, ponaturY,amp; ubi K d exterioremjX.Quoniam igituranguli D T £,amp;e d Hfuntæquales,crunt arcus medij amp;nbsp;minons circuli fupcr quos con fiftunt fimiles. undedetraCtisquartis uidelicet R F, B G remanebuntarcus F Y amp;nbsp;g h fimiles, item^ arcus x z amp;nbsp;G L fimiles. Patetergo, per exrimumuel per inomû dçferiptû ad libitum. Médius eadem uiainuenictuqfcilicct fumpto areu c z,uel F Yiecundum diftanoam cuiuslis bet eorum à rec7o5amp; dueda K d x, uel T Y D,ters minabicur femidiameter medrj, qui pro redo ponitur in d . Amplius, fi unus inuenitur per aliûjper ipfum fimiliter alius inuenietur. fint cir cacentrü e , circulidudiabgdamp;chfk, dus dis c F H K diametris, ducantur lineæ G D ,’F D z Sc F D.quiaergo nota diametro E G,8Cafcu G nn‘ j nbsp;nbsp;T,indes

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»s« P L A N I s P H AE R I V M

T, inuemetur e f , cum fintKFamp;GD xquidi* ftantes, erit angulus z F Kjæquahs angulo g d Fadeoarcus z k fi mill's eritarcui g t,amp;ob hoc notas, amp;nbsp;fîc conuerfo modo, nota E F amp;nbsp;areu K z,duCtalineaF D z, habebiturfimiliut Spalte nus. Itaqj per redtum omnesd æquidiftantes l'nueniuntur, SC ipfe fumetur per quemlibet. N ullus autem terttus per alium inuenitur per eorum diftantia. Sit itaep tertius L m circa cens trû E, fit médius loco redi, tranfeat^ linea F v

L Y.Dico ergo arcum K Y non elTediftantia ils lorum in fphera.Efto ergo,ft fieri poteft,et pro’ trahantur lineæ m L, G d L. Quia igitur K z fès cundû hy pothefîm, eft diftâtia extremi ad me« dium, erit z Y, ut diftantia medi) ad tertium. P,oniturautemQ.M pro ipfa: quareangulus M L Q. eft squalls angulo z F Y, ièd totus angulus

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K F Y,æqualis eft tori angulo F L M,co quod lis neæK F ÔC l m funt gquidiftantfs.Rclmquitur ergo angulus G l v,æqualis angulo K F o,qua« re Só angulo G d T. fcquitur ergo angulum l d G æqualem effè angulo l F g . Idem patet crie falfum: qui'a quatuor pundis d F g l , dreunt fcripribilis eft drculus, in cuius fcilicetdrcunfe renria funt illa pundra quatuor. Etcum angus lus G L V, fit squalls angulo G d Tjangulttsc^ L D G, æqualis angulo L F g î quia cadunt in cun dem arcum circuli prgdidtfquod falfum eft. Si autem alius preter æquidiftantes à redo fuerit

in plano ponedus, amp;nbsp;fuerit trafiens per polos, haberi debet ubi redtufecetj atcp redo in plano des feripto per centru, 00 per fîmiles dus ft dioes träfiensjinea reda,uice illius redi habebitur . Quod fi ille obliquatur à polis,tune eritcireu lus qui per polos di dos fphærc tranfis bit, amp;ipft fit circus lus A B G D, circa een trumE,erit^ corns munis

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munis differentia eorum illius circuli diameter qug fît B D, poli^ ipfîus fînt z T,00producana tur orthogonaliter a G, c F diametri, amp;nbsp;erit c F (èmidiameter circuli redi. Item linea contins gens L G K,trahantur^lineæ A B L, ad K. Quia igiturinarcubusT AD,amp;z G B,quiàpoliscirs culi B D ueniunt, funt aSC G, eruntarcus A D G B diftantiaeius minima à duobus polis: lèd amp;nbsp;arcus D F V B c, crût maxima eius declinatio à reóro.undcamp; æquidiftantes circuli per b amp;nbsp;d tranfeuntes, ipiàmcontingentlineam, quâ pas teteffediametrumin plano.Et ipiâeft linea res lt;fîa,qugeftuicecirculi a b G d in eodem piano.

Sitigiturin piano circulus redus fîgnatus no# ris A B G D circa centrum E,ôô fît linea B e d uice circuli pr^didi, per polos quatuor trâfèuntis, amp;nbsp;orthos

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ê^ orthogonalitcrcam fecans, fit A E c ,Sc circa DfuinanturarcusDTfimilisD f,amp; BZ fimilis c B,amp;ducanturlineæ AT k,a n z,ÓCcircundu cantur cfrculiKPN h,qui crunt loco æquidi« ftantium.qui in fphcra circulum datum con« tingebanLCuius circuli diameter erit n K,ut fu pra fuit L G k: quare in medio eius pofito cens tro, defcribitur circulus uicê eius in plan o obd nens.Quodfi idem circulus in fphæra rcótuin per mediuiècet,palameft,qubdetin plano feca bit, uthic circulus ak G M,cuius diameter in fphæra eft d e M, cuius eft comunis iedtiocum redia linea A E G. Palam igitur quod omnis cirs culus in plano, prêter æquidiftantes per duos eorum habet inueniri. Et licetalius co rum in plano ad libitû ponatur, ad reliqui defcriptios nem oportet primo redfum lumi, 00 ideo ad quamlibet dcclinationê habendam,eft haben« dus redus. Ex pr^didis colligiturratiojfecun« dum qua circulus cqualitaris, öd duo tropici,fi gnifer öd horizon in aftrolabio depingantur. PVndi,cuius in fphæra à dato pundo cir« culi redi, latitudo nota eft : eius pofirio in piano nota crit. Latitudinemeius déterminât arcus circuli per polos, Sd fuper ipfum tranic« untis, qui arcus eft inter eum,ôd datum pun« dum circuli redi. Sit ergo redus in piano AB GD fuper Centro E, 8ddiameter b d,fit loco circuli per polos, 8d datum pundum circu« oo liredi

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!»• PLAN I S P H AB R I V M

; nbsp;nbsp;nbsp;’ ' nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;li rcÆtrâfeunns^Et

fit illcpunctus D, lari tudoucroillius pun Óri ex D, fît ut arcus-DK. Dudlaigituror thogonali diametro A G, amp;nbsp;fîmilitcr pros traeù linca A k, fiet lo cuspuefti illius in H.* acquidiftas.n. e k, de fcriptus eft qui in fphgra peripfum tranfît. Ad huius igiturrei exemplum, poli omniucircus loru declinantiu à redo, inuenietur in piano. Circuli notac declinationis àredo,diuifîos neiniphæra habita, in plano quoep ha« ®beri potent.T ribus modis probat qcF dicirur, quiauel per lineas re(ftas,uel per æquidiftâtes, uel cir i culosmaximos.Per hneas redas hoemo do . Sit circulus in plano A B G D circa een cru T,amp; decliuis circulus fecet eum in A amp;nbsp;c, pundu oppoGtu per diametrum quæ fît A T G. fît^ arcus a d, quern refecat in fphæra,circulus tranficns per polos cum prima fedione decliuis circu li,quæ in cipit

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lO'RÖ'A Ni, ' ’ »it

mcipit ab A. Sit igitur hnea reda per centra, amp;: per D tranfeat in loco circuit tranfeuntis per po los,utlinea B h T d e, fiet a e loco prime fediós nis circuit A e G H, fed amp;nbsp;c H in oppofito eius. Peræquidiftantes hoc modo. In forma fimilis ter fit centrum e,amp; tranfeat orthogonalis BE D, 8C fumatur arcus a h pro declination e pris mæ fedionis decliuiscircu li, qug incipit ab A, 00 trans feat linea res da D H T,^ æquidiftans -redo defcris p tu s per T, fes cet decltuem in z:amp;patet

quod ibi terminabitur fedio prima: Per circus los maxfmos hoc modo, Sit primo circulus A B G D,tranfiens per polos redi ^ decliuis,ôc fit diameter redi AEG, decliüis uero B E D , fes dis^ arcubus D a g b , per equa protrahatur diameter H e K circuli maximi, cuius poli funt T z, dudacp linea T Z.Dico ergo qd* omnis cir culus maxim us,cuius eft diameter T z,ueltran ' fit per punda fedionû redi 06 decliüis’, uelæs . quales arcus de ipfis fecat,fedionis uerfus,quia ipfi æquaUter hinc indedechnant à circulo,cus oo * ius

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P L A N I S P A E R I V M ' lus poli funtTZ, et dus diameter T E z. Nam an guli A D L funtreÆ, ettotahs anguli G E B diiti tiaeft^æqua.Etiâi'ntdhgeqd' g e,h e, b e fine tanquâ quartæ ei» eulorû maximoru in fphg ra.D uo itaep trianguli ex areub. eirculorû maximes ru E L CL, E L R, funt binorum angulorû eentrum,fuper uno areu confiftenrium. Igitur reliqui anguli Ss reliqua latera,funt æ* quaha.Repr^fentamuscrgo formam fuperiolt; rem. Et quia linea B ED, cftuicecireuh per pos los tranfeuntis î patet quod in eafunt poli T z. Sitergo arcus d H,æqualis arcui A z,Só pertran icathnea AK H, eritep klocus poli z. Sint itêars cusALGM^quales primæfcÆoni arc euh dcchuis, quæ feribatur arcus eirs euh per m K L qui fueritMYK LN.amp; quia diuidit réélu peræqua,amp;tranfit

ipfeeft utarcus ci» euh map ,

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IORDAN h

ximi per polos T z, amp;nbsp;arcus rcóri Gmiles A l amp;: G M in fphacratratifèunris. Abfcinditergoamp;A N fimilem illi,qui eft decliuis in fphæra, quem amp;nbsp;ilk æqualem fcCtionccirculi redi abfcindit Ethoceratoftendendû. Exprgmiflis apparet rario,per quam in aftrolabio fignifer amp;nbsp;hori* zon diuiditur.Etin fîmilibus fi militer.

CVius latitude,à dato punefto circuit decli uis in fphaera data eft ,eius Scin piano fî« tus,cognituserit.Eftocirculus AB c D,perpo« los circuit' decliuis, 06 redit' traniîens. Dia^ meter redi fît A e c, obliqui uero b e d, amp;nbsp;linear Kpquidiftetei, amp;fît arcus DT,uelB K, ut: latitude eius de quo agit à decliui qua recirculus equidiftas à decliui cuius diame tcTTK trâfît p ipfu in fpbæra. Et pa arcus c B, A D ellenotos oportet, fîmiliter B K D T notifunt: igit non erut a tg K., Sit itaqj circulus redus in piano deferiptus a b g d , diarnetri a e g,b l E D K,decliuis circulus L A K G,fumpto^ areu d t affimilê b g in alia figurati5e,quc eft declinatio obliqui a rlt;do,amp; duda linea a F T,eritF polus circuli decliuis A l g K.Itcm fîtarcus B Xjfimilis arcui D Tin fphæra, amp;f D H fît fîmilis G K,ôôdue oo i dis lis

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Ztis Unds A P X, A H Y,crit p e Ylinca, 06P Ydia* meter æquidiftâtis decliui. Diiiifaergo P Y p^ medium, amp;nbsp;pofîto ibi centro,drcunducatur P ,o Y circulus, quieftuice circuli æquidiftanris decliui tranieuntis per ilium, cuius latitude à decliui circule data fuitSit^ N pundus in circunferentia de# cliuis circuli à que ai tenus latitude fumi tur,amp; pertranfeat lis nea N E m , eritep in eppefîtum ipH N in fphgra.Dcfcribat er ge arcus circuli, tras feutis perpuda m f

N,erit^ bicutcirculus maximus, qui in iphgra diuidens decliuê per gquaIia,trâG't p pelü eins, E quiatrafitperN, tranfibitetiaperillud,cuius latitude fumitab n . Ergo in comunis fedione ipfius,et circuli P o Y,hoceftin ó critfitus illius,qcF proponebatur.Ex nunc didis perpendit,qua ratios ne ftdlg ponuntur in reti,refpedu fi gniferi.

tLANISPHAERII lORs

DANI FINIS,

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