Dit boek hoort bij de Collectie Van Buchell

Huybert van Buchell (1513-1599)

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• • nbsp;nbsp;nbsp;de rug van het boek

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• • nbsp;nbsp;nbsp;de staartsnede

• • nbsp;nbsp;nbsp;het achterplat

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«,

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

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.

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

ft

breue, S^tuam me bcncuolcntia Ion ge inferior rem,immo ea ud autoreipfo placebit,ud exem« plojud potius utroq;. Autorc,quia hanc trada uit Produs, acquis Piaromcus, quia Arams, in quemcommentari non eft dcdignams mathe* maticus fummus Theon Alcxatbinus. Exem# plo, c|uia Cicero Sgt;C Germanicus, is impn-aror amp;^ familiæ Auguftæ, ille orator confularis Phap nomena latinitate donarun t:quia Linacrus tra duélionêhanc uiro principi dedicauit Ardu# ro, adeo nullamagnaingeniaexiftimaruntifta ftudrjs fuis indigna. Sed pracftat omnibus can dor mus.Is in gradu rennebit opdlam hanc,amp; in numero aliquo habebit, perficiet^ ut agente hoctuo nomincfufcipias 0óames,qucmamare hadlcnus,uel nihil agentem pomifti.

DB SPHABRAE SOLIDAI

conlkuälonc

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

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

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.

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

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

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,

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

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

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

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

«« 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

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«

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

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

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

•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

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

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

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

C x

DB SPhABRAS

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*

CONSTRVCTIONB. nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;ti

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. '’

ft P Ó K A 0 V

Sail Ka^âw ’Tfi Koa-t^js » J^tiit^i-jjoit ed/r^^vi glt; «p s^itfUTM, T« dè Tin^xrct 'rw «fuvotyTpó' ^ot ÄtyotT^ -Ttf K0ir(4V. quot;nil) j TsrÓAtm/y ó pJ^ Ai' yi’nu ^ófamp;os,o dS vórus.Jio^ios {jd^i’^ó d^ Tffcugt; •ns ^M,i'óiilt;^lt;^,6)S w^ï f^ »fUTt^ew oÏKMo-tp. tfórtos '3 « «^ TTcenós ió^XToSyiif Tt^s ^ »^^^^^^0|/ i^i^ovm.fîa-i pii} tbi rO' not Ttuts àSï ^^»Sy Smv o-vf^^odt/et T Tsra^ w/zZp TsriAop viJ Kft ifcw'cpopy iKttifots ió^X70y aveu, “ni/ dè Tirx^ »fuif nriAo/J a^xToit^iKéivois ^xvi^ôi/ aveu. n^ nrctAtpy isi Tts rinot uù^ THS yas^Sna iTvo 'BrÓAot óiiotusu^ iW i^i^ovros KavnUt

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.

£ «• AI P A* nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;ir

S C H O L 1 A.

Z»f.) Axismunilitflutl'meaA B tranfmilJaimagmaruptr ffharam. Kuiusaxisfummafignafunt A B.^r tjiûdemRpolusbortalit.Aauflralu,

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,

Pi^l tref carets KVK^Up.

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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,

s «gt; AI P A. nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;»r

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

i« P P Ó K A OY

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;,

S o Al P A. nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;gt;7

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

it nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;P P ó k A or

^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

Bolßitialib-

Z ♦ AI P A.

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

Atx 71 tirt^Ti pigvofi ‘^«2lc9Ji.oi c^ Tu trtjxxjt^at kukKh»

pt^n cfè 7T^o:ZA.ï/A(3;/zflVöi à(^CT^ïJƒa^öt'TKZ ttvuAot ets '^ vepcùfXiJ^ ^c^“^ laovop tvtovs ÿv tu KÓcr/ai^ T^aMiAï? w. i j^ »Kus KxT tuKsup Hpii^civ ais Tt^s M^ÿaip KVKÂop tsstt ^X^HÄOpt Tn^fts^iep^TDa^Ti} itrtixi^ivi S)fï T^'? Koa-ptv yivopli vluj Tpd^^o^bitySisi fH’rxfv ^ fgt;07rsKcö^ üvKÄaip q7r.lt;fis kv^ kAjss i^xfAuA}ss y^xepiä^ Vïrè r Hhtif, 'amp;lt;roünvi ^oCf «fai^at ^irtp CU ixiTxfy 7ä)i/~ßo7TÜp. eptfOVTOu efè t(^ Tatwrdlr os «si ft? oSt Tsrx^x7itHA(op KVKÄcop Kxd' iKXSHp upti^xp. ^T^t (rvy.gt; fiXTay^atpovrod JÏ ovTtoS'utxvTdlreisTfur creptû^xp.,(f^7à Ts^s K^AxsTr^xytaXTOiXSTÜip/c^7n xs^oAiy'iqttffoTicxlt;rv(x^ ^x^i^^gt; Vt/è yo^ KXTXSi^l^HVXi tfvVXTOp KXAcós T^ trtptü d t ^M

few ew^i 'tffeWTUp ^ -i^xTi^MÂCHp KUKÄIHy^ ^jquot;^ f^iytS^ K^ V VUKTÜlf •¥ »/4ifSlVTi KK^lCùs iV^iSluJKiy KViib Täni ^Oii^Hy ItSjvUüi/ KVKKimt'.'^S tMroi T^ quot;^ÛtIjuj ao-xriuylw •ƒ isfo^ ytKS ÿ/èiJ x7roTihilt;r(jex qii^ó(jSb/otioi/ ^XTxy^x^ov’nu yz th a-g)cü^lt;x,i)t Jè TffkvTi •^xXKt/Äot KVKÂûtyi/l^ 50 xTro'nKtxficcfx vii/x Tifoxt^t^i:^ /iu^ix(jJb^x dg '^ Tefonlw àtrxyaiylùj ■/ KS^i}^SrtXS-,KXTij^X!flHlt;rX4f àg T^ {r^xéfXi/.Ó ^ yo^ X^KllKOg KVK^og xifa^i^TTc «à éite^ovplLvx ^ xs^ai/.o j SiQtvègJieTri' Kog KVKhog T^ygt;07rbli 7ri^iiya,(^ Tii^xg èf^'^^ hAÏh 7röï xf KTO^i ßZTxSxinugtO 5 icTKi^i^tvog û.yK\sg rieg îanf^i^îxg m^tï ya/o e/è yit^i^tyog T^ayrtKog KUfiÄogyTi^l^x ^ ^ 7^? t^^x^tJ^' C^ixv TTfoxe^ÿ rS HÄtif), t^ rlà/yafn^ivH^fsTrb/j TCifny«, i Zé Xi'TXfKTtKOg ^wKsg TW (lt;H 3ia)§i!(.liVX Tip XS^Xp X^Oft ^e.iyavTig ovy Ki^xÄxiX uftxi/SLvx ty KTTOT^hiauxrx 7r^g riuj axxyuy(jM rüg Ks^oKeylxg-^lt;i^\üy lüg KXTiyfxeftxeiv èg ritv o-^M^xi/»

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

s 4gt; AI P A. nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;}f

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

SCHOLIA.

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

*/lH^ aa^ *^t^}iz^ }3i^%4^lt;^rlgt;}ym^ )U.4f^tSo âa^ J^arv joz ^r/»rlz'ß 7^ '7t 4^ Tu-'uri n^^ri 53 sh^tiéiity» RyTtnTi nyo ^ ism ‘5lt;u^ ^Z4rizi. Soz^o^fSo tjit od:^ 5oyvnn 507ttJ40lt;£S04t^3^ 0 4x/ip^rJo t1o^po d 1^ jä^ ^ ^ 'g ämät^'irlHJif ànSm vi^vnn ^ jjx 'ï t i^ut^ àmni^zTiHJfi ànim zm^^rZ» d»si^iri m^ 3^xyoyi» }fi^J7^S7Xt^ ^ 5/iJ^ingt;i. C. Xï 'rlr£3 njiD^J.^ »o ^ƒ 5öïJB§‘iix»5 «JZ ^ ^ ƒ 7}1^)^'SA7V'C xl^^^23^ ^^VM T7lt;th7,llgt;?,Ss 7l)tJgt;M W ÏX j^ji'Si^^gv^Tf m^Tto 7ygt; »S7y»7i ïx àojgt;0 /^ ^^Smzno /Jt4gt;Hlt;i7 Stifyri^^yxt]/» styvATj gwJ4olt;^ ß^^^^g amp;x. c^ö-fr^jïE’/?»ex»ry'C 'ViSu àn^oâ'mtb â^ mjJ. TV^^TJ^M^nj} 50iv^ o t^ ^ttOyf V7ffy7t oc aidSUé ^ 5lt;^ ♦ àu^ Mirs. ^ '^C ‘■^^Z477^r/x)yoJiX à^'C his^ »jx^^ttriz Q'i 'fiSiri’S S3 g^rlaJTXni/i n-yx/^n nyo ^ ^sm *•50}^« ie.Z47i-U. ^X40^gt;Sj tSU. Mi^ SOMUodl. SOAl^i^ o âlXHTIW àX^^Z^Titt r^ ^ 1^ ’ ioC^Ó^fSo (gt Od^ 50^71/171 5O7(tJ40cÏL 504 ^j^ig o S^3rZ^üXi^ M ^^n^37(àxri» Tnot^iixi^ S^JZ 5tJ^ »5 ^nX ^ 5»SiS!L T^'rTU^UTiXJ. 504.40^1^0 ISgt;X^ 0^ 50^7(7771507t1Ji Ci^SoAiSz^ o uS^rZ xiunxt 53 ^àt4gt;Z7(W àmrZu rZoyyXrZ/notJ^rZHJt 'iri Ja^^ 5iojL * 77ai,74i'C /ZkXS^m Soy7tn7t soTtwoc^Jo/u^zç a 5tyoü ^‘5?x xSnX ^ 5X^740. ^ 'SOJyto'^fdo ^ oa^ âo4tlt;Siç âa^ ^^747ZyL B47T0^rl/ix uS^rt xSun47t4X 53 âtxxTtio àxrZu àoyyXrl àoCK^X 5^ z^ ^ T^'TOO^UlX 34n^rZ/lX àuXoS'iSiA ànZX7t

V nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;6/ J » gt;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;i 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;1' * $(viorio â7yü^ ^ zwSwY C /?y^»ja |^i ^^àu'C arfz affi;A /iöÄ’JOY» C, c^ ‘r»x,ï/w^r/»gt;vej2» rtu'C Sï-CSA vri^jb '^^^^ ^lt;ÓS’'^ “^ ^ '^^-^ lt;40^1^ ƒ lt;U2A TALZdrlyi, x^t^ 6^^ft 0A^ Sü Styitnit So-xtutcil^ fsarS'iÇ ^ o 'TiiLz/m^vywx àugt;(. ^jm. scyo SoyunTt Sowi-v^» ^^ o’-àmyxnit àmyu'tiivSxsa, •^t.^so. än^u^soJu, ^ âmj,

'ämyitnv àmy^u'fiv^

^^^^^ n'^ Sm-p/idu 7^ Sxs/ntKÏiwi^ thû

•tnuiixp mujflo^'MTvpujcjiidop snTjiiutiff ^IvXi umtjoou £) iitniitp uuipmtuSpiu iip 'uipjügt;ifJJ ut jtmupijuoJut »j ji^fopoutonb (,'ui7pi»his ’snuitxip outtu ifojip unzpnb unuonpjt npuH9 u^ ’uliluPiftpmbxjzifzpjijJipziniamp;jiiiui pin]ott37pdfijijjptiiii ‘}}JtoJ p]]3^

AOVaOdd «ï

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« cÆ ?! tAuu^iinui T«wTÿî «xaAaSà lü/ ntyisltv »lii^ccy ^ Pid^^Oi yivi^ u^àgt;y ia-Hfii^iviii tZ» K^ HitttrVy tIw ^^ n/tifct igip io-HiAi^ivSiiJ 9.1(9« »luav. é o^ ia-Hiii^tvàs IcvK^i kx^ thliU tIÙj oÏKSpSii/luJ lt;AlJ(0amp;li^TTU. VW Ttf Ôô/^OVIOf j ist Hia KUKÄlty ^nÄ quot;OTtg yltjj KTnkXliScWi^W^ HlUKVKhUIJ (Zi VXirâ ^(iv, «A» hü MTtXi) u^ Tfil xvKÀZf TTVTZf cû ïtrfUJL'iQ/.ou. ytvoff^-0 Jèyau'i^ivos ’JjiOTrtKoç Ilvk^s \sisn 'Ti^ oQi^vamp;i tzijlut^ «VTtos, «îTt 'n ij^ ikxifsoi) T(iH(iX •^Ig yluj yiv^^^t 'n lt;fè. |lt;è^o(/ 'varo yhdi. « ƒ’ xviaoms ^ ’riJLHiiXTUt» tZw cdnrlù) 'tax-fxT^xylùi v^a u^ •wxvTuy rStp KKilixraiifi »'ns tylv^ famp;i tuh Ttf 3tgivaG quot;ipoTTiKi KVKÄv. J^ Tsrewns yo^ 'ne ^xTi^à f ’riihiAXTX T'j^aTriH'üy KVKKay !amp; à^AwAsiç ’tó-, lt;/li bu tà'nxif H myisK Hiz'ipivH^ ’ta-1/ K^ ?« yc^yisH vvK'r^tvH^}{^ « i^xyisH Mtii^tvu^ ta-n m ihxyisH WKid^tvn. o Jè ewTX^KHKis KVti2ss o^S quot;v^ quot;ny i^ÀlÿVTx liÿÿ'^i.'rou»

DE OCCVLTÄT1ONE ET EMER»

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

3(4 nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;F P O K A OV

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

Z o AI PA. tr matibus uarietatê habet, quam etiâ in fôiftitiali tropicodiximus. Semg enimreipondentesex aducrfo tropicoru fcótiócSjgquaIcs interfefunt. Eo^ fit, ut maximus dies maximænoefh, amp;nbsp;mi nimus diesminimscnodbacqualis euadat. An« tardicusautcirculus totus fubhorizonteUteu

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.

Tipe/è Tr^act^ttpAitop tire^Ti TFctfctfiKHAtoi/ KVKAup^TtvZfi tl!^ 7« (ai^i^ÿ t^’ Shlut liu CiKWpSijtljJJ e/lutpdivi TK cdtra. ' ^ Ci Tlfilf

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

s e AI P A. nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;Î7

^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.

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It PPÓKA0Y

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

}gt;

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

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^

s « AI P A. nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;41

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

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

s o Al P A. nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;'4,

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,

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

•lUOH ta t J

’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

«y d IV «t S

4«

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

s lt;Igt; AI P A. nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;47

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

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

s o Al P A. nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;49

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

P P Ó K A o Y

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

£ 0 AI P A. nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;tt

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.

1 nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;Ptei 76Ôp tiss^Ti ^cavuip..

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

n nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;n p ó K A OY

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

V

s 0 AÎ P A r, ftgnis KL defcr'ibunturutTintjue. Ipfalongd.) Stcundumhypothrfim, quad ßadia D. in terra dantgradum mum uMtma anunferemia cede* fiii.reddunt centum M.ßadtorumgradusducentosfvfier aquaiore.AtPtot lemaut extendit orbem habitatum inter occidenttm CT orientem gradibut chexx-ßue ßadtß in terra xc. H. differentia eß inter utrunef ßnemtradur «. ßadia autem x. M. Lata autem. ) Dimidium numeti priantfunt ßa* dia mille quinquaginta/td eß,gradus fuper meridiano centu. At Ptolenueut ßmt orbem habitatum uerfusJeptintrionemfub parallelo,^ ißante gradibut bai}.uerfus autem außrum ultra aquatorem paraUelo dißante gradibut am» fhut mi.facit latitudo fuper arcu meridianigradut txxix.ßadia autem ter» ra xxxix.M.qitingenta.Porro Proclut loqui de téperata uerfut feptenti ionem folum uidetunhiec autem ut latiffma accipiatur, comprehenditur inter pa» rallelotduot ,huncperMeroên, illumper Tylen gradibut fuper meridiano xlvij.ßad^tuerom terra xxvij. M.quingétit. Adhancrationemueleorrigan tur numeriProcliani uel excufert irtquoniamintantit terraru fpatyt, dein de commentaryt,o- tabulit terrenifitut diffrrentibut donandum authoribut tßft quippiam calcula mdulferunt, fif fequuti diuerfafuerunt. Utiamficut ueteres omnet cófentiant:tamen noua bißoria cogniti,hac atate quaquautt fum orbit eot omnet tmendat.

Pi^l TÓSp KXTiSH^typiSiviUp ^efffop»

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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

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«

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

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

rd

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

«• 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

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

« 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

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

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

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

«^ 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

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

«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

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

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

- ’ o P E R A T I 0.

7«

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

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

•HORARVM' TEMPORA blVU LATITVOINIS »K, ad media (îgnorum, atti tudincs amp;nbsp;umi bræ.

HORARVM ÆCyVALI^

VMAB OGGASV LATlTVDINIS xly.ad initia fignorum, akitudines amp;nbsp;unibræ»

Kefiduum («bidti ftlt;pütifft

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,

K Isnu

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

o P B M A T f 0.

W

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

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

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

K » us,Sed

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

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#

nu

«o

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

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

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

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

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«

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

«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

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

SS

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:

B b ROSI

O

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

m cors

RBMiCÏC. BEROSI

correct um hcmicyclium confirmetur. Vfus d« us (ciotherideftjUtlincaipfiuscardinis flatua* tur in planidejn Kneam dus nominis dudiam, in plande ad arrifidum,quod ddenbit Vitruv uius libro primo. Frons autan c, refpidatau^ drum. Hæc ita perftringcre breuiteruoluimus, Ódnemultadefiderentur, adiunximus febema, quo reliqua exemplo repræfentemus.

FINIS.

»xoxu f tu

^Hotrgrioytznvd 510^ äerliM^tu. S^JZ Xy^x ‘Susi^vrlHArfei'n o JoSoj^s iJiii) 5n*5^^tSn» lt;u. 5^^ no ßt tzo ^ »j.Bjz.vngt;JjAuyi 'B 5»gSo ämy no'5oi,v^ y o ä^JiU^noxfit« »sr^ri 510 ^a-^o^fn^ »x 7^ öji^* W äozKÄi0 C. ädJM’flB^vn ämjLnoz ti^ 'ämt^ 'jv^umj) f^nzyojß ^ wYSmiu^i âmj. %XX5 rs? 5w ‘tox^Sb SM^vx nAVsa, no '■»^hSb A^v^^ nj,âmlt;îs» m r^ ax rxo yt f}o3sgt; ''niß'^nviixtvzvx äv^ii-o /rTjd^rl^MS!i.n rrrjz äodtotbrlna äm^fi^ ämz äosByai. iqn nex ‘ âa^vmy) vstyxii Sm »^^r/ox»5 ^Ji Sarit/ fit v^ ot^p 'wno/tmiirlnjj no m^nv^SiesBysa. Suz ^ tr/pi 'vb'i 7^ 5m§»x *njx4oY’SY nexn» jlx Smrlndm^xji ^ «j/» oi^ 'i^oijo^ V âî^SmiiVX) ânod iu.S^ii.^ni^i)-Dnoi.rwioz ^lt;^ t)»J3H^»0A‘iJi^^ toi w^ ‘ ni^xmygt; äa^nyow^xsa^ J^VJ ^ypxTi Ç 5»4?x 'ämA^o/Czy âmjL ^BAxtit^ Sm^^np a^ asj ‘»öxxSm 3u, àmJAOotxmAtiCxdM vstyxrl sm^mSió ^ ^sm^t^noAntbrinj) « ilosayji 01.1^^ mix^^àwti. ilz (Joxs Sw) a^ nrwizyojji ^7]o5nlt;tgt;D nArjprIoSzii} ilna rv ‘»^»0 Sm^S^ wdXsu. ‘â^/nx^rluyi '»i.))x vg)plo/Ciy xi. n6)i f^toyn^rl zjB ^So^Coy o SorltDu^ 'xai. 'xi» ;^ tJ)noxj}m4ilt;Cvnx vsryxrl Stoi.mlt;Sii. swi. tip àoy»^ yt 993? • àmyMXZ dxirln^Ot^ â«D m^i nrloXS^ ‘ra^^x^ noinoj. »^ »411 âo^oylót ^iDSiyvx»2»s2. ilm^wi.3àmiS34ti toyyx ^ nigt; nSh ’p^^^^ m4 *frr^lt;tgt;^^ ^^Qo ^se^od^^z So4ti Sxyó^ ^x ax ^ mjti^ • agxrloytii} Gt ncrlp^m^pyoi^x i^yo/no lt;mxjsvyöK) ,^ mt^ist.yï^Sodrgrló^V'CJ^ àx5nigt;D X4ii nrjiirxtai. ^ S^ âo4xK jni^ • Stoir)plo'Czy noixJv xi. OJS^ S^oi ào4miirlnj) âaXiâtx^^ *noxxiifin'p HZ xS^Tixz4oyi‘iz»/mSp^ iz^^'Snoyvnx Sno^ '0ii}xS^ nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;tiz t^ Snaz Spamp;. rßk *ïX »vp

'nyyxspoiu, xiy»^ liznv ^ xzzsm^Smzno^^ mxxnzxxvzxu tna^^ihß äxazvSx àozvd'^ 'nytSi/p^^SoytopYlKaStzB si4X^4ni!.^‘gt;^^t Wamp;»ii^K S ‘»O/JïT^o^aYJï mt^Msv'Ch mw4xXHrl J^j^ ^ 4)plo4xX'Cnz^ iSm/p^Q 3yxx n nrjmd.

*3VdIV4gt;3 SVIHiVdV SHA^MS

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