Sphaerae atque astrorum cœlestium ratio, natura, & motus

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breui nddmawT^illd1*\>*,m eandem commentdtio Theo

nis , quorum utrurnp opus iam m mambm habemus : ut interea dtjftmuUm

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conftmdione,

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De canonicaper fphaeram operatione,

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m eentro liuram dflignato. pag.zai.lin.x.ad Hntdm .

IACOBVS ZIEGLERVS LAN;DAVVS BAVARVS, PAVLO BOMs

BASIO BONGNIENSI S. D,

VominSapheam comentarcr,

pollicitusfummeetiam icriptu?

rumin Sphseram Archimedis>

quam ego ei autoritnbuo,quo*nia habeo periiiaium mihi, Ar=

chimedemprimum uel coftituiflehanc, quam

folidam dicimus3uel collocaflein eam ftellas fe*

cundum canonicas radices, Eius ergo conftru

dtionem daturus prxfenti opera, faeram addi=turus etiam iiagogas ccditus apparentium re^

nimcircumtetTenahabitationem^uemmquia

ueterescum alij, tum Proclus , quorum ftudfjs

conferremeno audeo,ueriati in eodempropo*fitoiunt5 aduetereseamegopartemremifi, de*

fumpficpProdu quihanc abfoluat Addidi ta*

me locis opportunis fcholm, adduxicp fenfaau

toris ad defignatoru in fphpra circuloru cxem*plum manifeftum, Quademu iiidicationcab^

foluta,fubiunxi quaficoronidepauds capitib*

quemadmodum canonicaratio coeleftiu mo*tuumrepr^fenteturin propofi'tafph^ra

5in qua

etiamipfi operemureofdenieflidus concordi

iymbolo,&quo eos operatur in coelo poteftas

nature. Hanclucubratione tibinucupauiPauleBombafi amico benemereti Neque ueritus

fum, q>abie<Surus fores opellam hanc, quauis

a br&

e DESPHAERAB

breue, &tuain mebeneuolentialongeinferio^

rem 5immb ea uel autoreipfo placebit,uelexem*

plo,uel potius utroq> Autore,quiahanc trada

uitProclus, atq$is Platonicus, quiaAratus, in

quem commentari non eft dedignatus mathe*

maticusfummusTheon Alexadrinus. Exem*

plo ,quiaCicero Si Germanicus , is imperator

&familixAugiifbe, illeoratorconfularis Phas

nomenalatimtatedonarunt:quiaLinacrustra

du&ionehanc uiro prindpi dedicauit Ardu*

ro, adeo nullamagna ngenia exiftimarunt ifta

ftudijs fuis ndigna. Sed praeftatomnibus can

dor tuus,Is in gradu retinebit opellamhanc5&tn numero aliquo habebit, perficietcp utagentc

hoc tuo nominefufcipias& ames5quem amarc

ha(flenus,uel nihil agentem potuifth

DB SPHAERAE SOLIDAIconjkutticnt,

APteturfphxra abfolutaad femidrcufi dr*

cunducfti caftigarioncm 5fuperdiametro

non minori palma& feniis , fiueutlibitu cuicg

fuerit>& uifum opportunu. Ea fphaera fi exme

tailo efl;inargentetur. Sic cnim profunda drcu

lorum& deiignationu fient confpe&iora, Vel

fi ex materia fiet3parcntur tres armilla?cx una a**

quilatatione,qua^fintprcfunda:interius 5adr<

cunfcrcntiadigitos duoslatos, perharumme*

diasiuperfides fcribantur drculi utroSp earura

laterc

-« 5 R y C I . .

iatere,exuna gquilatatioeperfingulas iiiper

tis diametralib.A c d,& ebf, etCEDF.Inri

mamateria a cetro ad drcunferen tia infcriore,

& finientemprofunditatemarmillarumexdns

jdatur. Duarpofteapriores armiilx inferantur

mordicus mutuo in communib, punctis »His terriainducaturfecundu fimilia figna prio

rum cedf, couenientcp tres iiiper circulo me«dio profun ditatis,ficutunam &Caequalem red^dantiuperfidem fupremam, Relinquunturfic

quartae. uacuac, quas oportebit iblidama*teriaexpleri: uidelicctparanturcunei deiiibere,

quoniahaicmateriaeftarida5 necinflaturudis

auftris, nec dehifdt ficcis aquilonib.flantib.un

deuidumglobofierct. Cuneorumpars fiteli*

mata, ficutinteriori drcunferentiaparesGmmteriorib, armillarum, exteriori autem pares drsculo medio du&o. Pars altgracuneorum elimc

turjUtinteriordrcunferenaareipondeatddem

drcuio medio , id eft , conueniatad ambitu ex*

tmoremprioru, Verumexteriori5 fimiliter ex*

teriori armillarum, fuperpofitiqp fibi reddantmulprofunditatemaflumptarum armillarum»His coftipenturuacua lpatiaquartaru,interiorconftipatio ordiarurex utroq^Imtacarmiite c£ D F ubi ftatuanturlatera, defcendatcp uvcincp

cotra & angulos, copingant &confiipentprobe>& iniecfio glutino cofirment.Huic coftt

pationialtera>& quscexpleatglobu inducatur,

a i) tranfc

tranfuerfis cuneis, fic ut eoru frotes ab armilla

C D F defcendat tota iiloru proceritate. exple=

ds his quoque& conftiparis fpadjs^compagi*

netur glutino fubimmixto . Hac rationecund

indiuerfanitentes,efEciuntglobuperpetuuiri,

&nullauemfetefatifcentem.Hocperfeao 5no

tenturpunftaabutrinquefignataperfuprema

fpinam armillaru,perqjfedionem exomni late

remediam.exhis pundis fcribanxrduo circuli

fuperdiametris, quafi digitalib. pofteainipfis

pundis Bfigaturaxescraffiinftarcalami ari

ftge}aut eo etiam craffiores }

et exeant afuperfide

fecundum angulos redos.Cuius rei exame eft:

ftatuaturpescircinifupermediacraiTitudinea*

xiumquafi' centro 3altercxtendaturfuper circu

lu iuxta defcriptu- Is cirdnus circududus, ubi

manferit undiquaq* in drcunferentia, axis eft

correctus.ergo con firmetur. In eos axes fufpen

datur armilla, cuius diameter exeatperme*

diamcraflltudinemaxiu. Interiorautcircunfe

rentia fitelimatafecundu ^quilatationem fphe

rse. Eaergoarmilla transferatur perintegrum

globum, isfcp dimeturfecundu illius canonem

ad abfolutam fphxrau Ei caftigato inducantur

nemi tufi,&: his glutinum 5& ca?ra ,

leuigeturqj

rurfus fuperfides fphaerac adcanonem,&de*

mum inducatur candor ceruffe, &apparata

cft fphaera.

CONSTRVCTIONB. f

D S I G I S,

SVfpendaturrurius canon axes . con

ta&us diamctri C leuiter figneturfug fphas

ra, Extrahatur axes,& locacopleanturutdrd*

nus figi in fjs poflitPoli figneturmaiufculis \U

teris,&coloreiniigni JPoftexploreturpun

ftumfa&um ex c diametro canonis, ut fitme*

dium inter polos, 8cex alterutro poloru exten*

fo circino incurui crure in notam media ipha&s

raeicribamrinfignicoior€5quidiuidatdrculus

inpartes quatuor sequas cedf, Ruriusfa*

peralterutrofigno uelF fcribatcirculusinfis

gnis expriori 2cquilataaone}fuperfignis c

D,Rurfus ex altero pun<fk> c uel d fcribatur cir

culus infignis exeadem sequilatatione fiiper fi*

gnis aebf, Circulus acbd iiiper quartis di*

uidat in quater xc partes Inicriptio GtexE &F per notas denarias uerius polos* Item

maiiturarcus quatuorin diftati)s tropids gra*

duum XX & fanis fere F G> H5

F5& *Fixoq? drcino in L udl fcribat ex priori axjui*

a t lataticne

# D 8 R

latationecirculus infignis c G D , Poft hxc

duo circuli cedf,&CGDH diuidatur kcun*

duni quadrantes iri quater xc. partes, Porroin

circulo c G d Hfignenturtrigefimsefediones,

ordientes ex quatuormemoratis fignis,perhaec

fegmenta xrj. &notas l fcribanturcirculi ex

priori aequilatationeomnes infignes, hi partien

tur zodiacum,Si fimul totam fpharra partes

^quas xi>Scribatapud c Aries,fiuehuius nota

*\ fequeti fpatiouerfus G Taurus V- Hincge*

miniHT.ExtraG Cacer c^.pbftLeojl- poft itp.

ultra D Libra HincScorpius m- HincSa*

gittarius >7r ultraH capricornus^poftAqua

rius ^ poltremopifces x.Diuifionesgduos

circulosnumerodenario fignetur, &fquide in

circulo CEDF,fxC per d Fcorinuanumeri

fucceffioncii% in ccclx, Vlrimoex polis

fcribantur

C 8 R V C . 9

fcribantur atrameto quataordrculipermediafigna hg&l K.Ite exalterofigno G uelH

5 fumatur latitudo zodiad utrin^gradus vi. Scpolo: extenfioneautem perimgulos vi.gradusborealiores ecliprica ducatur drculi atrameto.Itcm L centro

}extenfioneautperfingulosgratf

dus vi.auftraliores ducant finguli drculi. HxceftdefignatioiphasraxErgoreponanturaxes inpriores iedes ,& corrigantur fecudumde*fcriptosex L&K drculosjhrmeturq^necppoft

hac ufquam moueantur,fintautemprocerimunus medio articulo digiti.

DB ARJilLLiS CLIMATVI.

PArentur armillse tres ex metailo Latitudofitutiuperetquaqiia ueriiim ambitu fpha?*

ra? tribus lads digitismidelicetpro mefura iphgnr

5quata affumpta pernos eft. Trium lamina*rumuna Gt quadrata, Dua^itiperent tertia par*

telatitudine.In ea qii£ paribus lateribus5afliim

ptoumbiiicofupereoeducanturdiametri

s & R ^defcribaturq? drculus fuper figno,

extefioR paulb mefura iphser^ :nempequantSoccupctgranum canabi interie&u>& fit infcxU

ptio exM R contra R & c in gradibus xc. fu*

peretiam extremo niargine fiatipatium drculo

rum , Id diuidaturin partes aequas xrj,& fuper

lineis edu&is ex centro fcribantur uentoru no*mina, fuper aufter, fuperR eurus, fuper s fe*

ptentrio8

3 D S Afi R Af

ptentrio, fuper c fauonius , Si reliquorum no*

mina ordinefuo,Gcut haecnemo no nouicRe*

liquc laminsc quadrent diametris, Seddu£ qu£

tranfuerfsefunt longitudini, diftetafrontibus

per menfuramfemidiametri tabulae prio*

lis» Vnaergo quadretur, &quidem tranfuerfa

fit s, quacautem perlongitudine5v O.AU

tera quocplamina quadrifaria diuidatur3&: dia

meter eius tranfuerfa REC, quaeperlongu

D, fug R D c fcribat circulus exprimaaflum^

ptagquilaudoneuidnafphasrx^atcpfemidrcu

lus R C diuidamrfuperutroq^margine5int€i

riori &€xteriori fn partes utrincf xc Fiatcp in*

fcriptioexteriorismarginisex R &ccontrav*

&inferioris ex V contraR& c. SuperauteM

S lamina fcribatur ex interioripnorum gqui

latatione circulus afbae, diuidatcp in partes

quaterxc ,& fiat infcriptio ex ae contra &.Abhoc extendat cirdnusad fpatiu prope lati

digiti 5&fcribat drculus alius diftas aproximo

non amplius grano finapis interiedois quoqj*

diLiidaturinpartesbis xc,&: fiat infcriprioex

s contra v,item ex contra M* Fa&is dimenfio

nibus circunddantur extrema tabularu ad ab*

folutam rotunditatcfecundu figna R s c m 5&

r c,& V s Interiora quoquefuper intima

drculoru deiignationeJtemarmilla f ae to

ta Ubereturab armilla fua ipfius fuperiori fuper

fpatio interie&i miltj, ficut punda fuperioris

non

C& N S TR VC Tl 36. *

ponuiolmturJPoftidcomponanturomniaincorpusunum.Sphpafuis axib, fuipedaturin armillam afbae in iimilia figtia, Rtxfin opereprobato diameterapudae fignumjredeinfi

ftens fupermedio drcuf Cedf iphaers&Sug*

ficies autem armiila^ quge prafert defignatioes,

ibitpermediu axem iphaorx. Pofthsecapte

turaxisipfimeridianoin pundouerricis,asquotanquam cardinepolari moueant quar

tseuerticahum vr, 8c

c. uidelicet actipiat

duplex craflitudoari:

mill^meridianiSecui:

dumhuius menfuram ducaturin planicie dia*

meter Sitquoq?propofitalamina,exqua a*xis perficietim In ea ducaturlinea C d contines

diametrum tercum & ex C D ducantur

perpendiculares CE&df* funganturquoqucF rc&a. Eius quadraguli duo laterace&df

fintlonga, utpattes. qualiumeft totalatis

tudo,fiueprofanditas meridiani HarumaiTusmanturduse &Tfemis ex C D &iungantur re&aG H. Eius quadraguli ghef duolatera diiridan

turin partes iii ,a2quas>&pun&aiungatur re^

ihs. SicdelineatalaminajComplicet lateribus CGE&DHF f&caftigeturad teretem figura, reddetq?modulum aflumptu elimetur fecuru

dum oppofitas ex diametro partes prideaffum

b ptas

io DB SPHAERAE

ptas per quartas ab imo pede F ad finem G H,

fic utfiiTuraarflecomplertatur crafikudineme

ridianijipforumq^brachiorum gehf rotun^

ditas complanabiturmalleoload aequalefuper*

ficiemfui &meridiani ,ficcp axis agbh extu*

berabitdecenter ultrautrinqp fuperficiem merii

diani, pr^ftabuntcp fequenri operi commodita

tem, Inde parentur axes duo, quibus duaequar

tsc R& c fufpendanturin priorem axem, in

eocpuoluatur, Accipiaturcumcircino fumma

craffitudo fuper diametro axis prioris,fecundu

eius menfuram ducatur in planidedimetiens

, Sit quocppropofitalamina exquaaxis perfi*

ciatur, in ea ducaturlinea c d trib.partib.&longioripfa , ducanturexC D perpendicula

res ce&df, Hceclaterafintlon^aadmenfura

priorum agbh, iunganturre&a F.Eius qua

dranguli lateracd&df diuidant in partes iirj,

sequas, &iungatiSrlineis parallelis: mediafitg

h 5quaeexeat ,

fitcp quanta G . Eius

accipiaturmediu fignu L,undeexeatperpendis

cularis par profunditari quartaeuerticali,iis:

ueea denicppaulo contradiorJpfi quotj? HLKducanturutrincpa^quidiftates pro craflitudinc

quamc.Extra has 2equidiftates5&: lineamMLNquicquidlaminx eft refdndatur. Quadrangus

lum quoqpcedf fuper linea

F

5liberefab

F

ab extremis finibus ufcp adaequidiftantes,

utrinqticipfi LK^antaparccfolumcoh^reant

CONStR vcrf 8» R B

duo quadrangula ; Pofteacedf ieuabitur, fic

utGH ftet iuperplano

lk ad angulum re*

ftumin H.Torquebit

autem c d f in figu*

ram terete, inftar axis

prioris, coibuntcp late

ra c &Cd f lineam

nam, reddetq? ea figu^

rateres interiori iiiacir

cunferetk modulumcirculi deicripa,iuper

fic caftigatu, uta^

xisindu&us priori cir

cumeuuoluatur con*tigue,neq?arAius

}nes

quelaxius. Laterade*

indeMl&nl fuglk

nasaequidiftatib, ipfi

L inclinabuturde?

orfumadangulos iru

teriores reCtosfupcr^

quidiftantikdeniqjfi

nes diftetmutuo

feamdumparallelas* Eoaxefa^

brefado, pareturaliuseodefche

matepropofito, quihuic indu*

tfhiSjdrcumeum uoluaturcorig

tantumutabitjdiuifalaminain partes quatuor,

b * ducatur

DF

II N

t «81

ducantiir ipfis C utrinq? aequidiftates OR,&Q.R paulum diftantes amarginib, Poftealamu

naredu&a in axem,fs elimetur toto corporeme

dio inter latera 8 reliquis paretur

Jcutprior. Quoniauerohiaxes in an*

gulis infiftut in firmius,cp ut quartis

v R& c ferendis fuflSciant5iuerit ne*

ceffe adderehis a tergo cathetos,ut

CErgo axis pofteriorinducaturpriori. Sicmu

tuo induclisjaddatur ipfis a tergo catheti, quo*

rulateraG fintpaulobreuioraipfisaxib.prars

ferrim in axe priore fecundum fpatium *fierioris, Fithoc opere, ut duo axes fibi gpetuo

cohaoreantvfic rite coheretib.omnes fimulcoms

mifluracconfirmeturillo glu*

tino metallico fiiforio. Demuipfisbrachrfs inferatur

quartsedux R& C in mo*dfeimhuncAxes G ftatuan*

turmedrjfuper diameirum d inmediamneam uerticis ,&communem duabus quar*

tis R &CV C, Lateraautem lm$>Cln deicen

dant utrinqueper latera quartartim, easqp arfte

comprehendant Diriganturautem finibus

&C. re<fte in centrum drculi5 ficq? corre&acon*

figantur utrinq? binis clauiculis , ne quartsed&moueriabhabitudine centripoffint. Spatium

quocpquartarum, quodefta diametro ad bra*

chia, umnq^refcindaturJntra hanceniminas

nitatem.

-o C Pfe

C S R V C I fi.

tatem fufcipieturcraffitudo armilfaemeridias

nx. Ambsepoftea quartse refecabuntur fuper

media diametro R C dereltquamedietate R Dc. Reftat difpofitio indids In affumpta lami^

na ducamr linea G longaut in opere fuperio*

ri5exearefecetur , ducanturaequidiftaiii:

tes qusefatisfaciant craflkieiarmillaram,*roex ducaturperpendicularis3

atq^huic alia

^quidiftas exX,Finisq? utri*

ufquetermineturfuper 8n. Porrbex xquidiftatibus

apud ducantur duaeline^,

quseconcurrantin G.Quio:\. N|

]

}

tra defcriptionem hanc reie*

cetur . Tuc L K(quod fieri

ctiam in iuperioribusoport€bit)reiiocabitura

rectafuperficieadporrionem cireulifecundum

conformationem circunft^entice umusarm&larum.Conus autcm G in bafi erigeturadan*

gulumreflum fiiper h, utapex G reipondeat

in iineam diametri edu&a ex centro per feffios

nem qualemcunq^armillaru, utcjangulus ma*

neatcorrecftus addetur illi quoquecathetus

g Brachiaautorthlm,&h ln demitteturin*

ftarpriorumadangulos re&os,red:iscg flnibus

iuis ipedarttibus in cmtrum:fic utcomprehen

dantlateranon quidear&eutin prioribus, ied

necglaxe: uerum iaftait contigue, &C moueri

b poffint

» S S fc R AB

poffintperc^ichnequartp, cuiindexpro tem

pore&Cobferuationeinfidcbit. Hancfabricam

axiculorum Si indicisfum prolixius& diligen

tius executus, quoniamno aliud eft ngenium,

quo hse quarta: prsedpue aptari poffint iecun*

dumcanonica organoruoperatione, 8i fuerat

meo iudido diffirilior,cj ut artifexeamexiemet

conciperet. Etficdeniq?diffidlisubi leuiter in^

choatardinqueretur. Admultaaute organa&

capr^ftantiffimatutpote adiphgra hancfolida

fugficici cceleftist adaltera fugfidei terr^: ad ar*

millas,fi libetPtolemgi meteorofcopiu,organu

l^hscrsemundanacjadorgana^fingularu fphc

rarum planetarum,tam eft neceffariapars haec,

utpraeterhanc iftaperfici nequeat. Sedtandem

poft longamquafidigreiTionem,adcoformai

tionemorganiredeamus, In armill^mrsc me*

dietateM R s,ducaturaequidiftansipfi s fecun

dumcraffitudineaimillsealteriusM vs D.Poft

exmterioricircunferenaautriiK^ apud mSCsuerfusexteriorem fumatur diftantia quantaeft

latitudo armillsc f , : hse partes dimens

tur.Pbfl:acdpiatur medium refidug armill^ins

tegreuerius exteriorem circunfermaamutrin*

que,& medietates cxteriorcs dimentur. Super

autem diametro R C,diuidaturtota latitudoin

partestres3cquas}&medi^pertundanturfuper

mediadiametro R c, \n armillae mdsv medie*

tatcM D s,ducamr aequidiftasipfiM s,fecundu

CCNSTRVCTIoNE. »#

craffitudinemdus mrs C.Etduslaatudomes

diaduridatur3 &medietas elimetur adrcunfe*

renriainterioriutrirw^apud &C s.Super alte*

ra diametro quse apudD defcenditinpedc mee

dia diuidatut (uperT,&medietasabafiadT elt

metpro craffidcarmillasr RDC, iugmedttlinca

D T*

ni D JS S AE R AE

t> 4 Sed Si irdiquadus medietas findat, uthac

partedidud dmaricaricppoffit In tertiaearmiU

\x medietateRDC ducatur cquidiftans ipfi R c

procrafficiearm%M RS c,at<^huiuslatitudo

diuidatur in partes tresaequaSj&extremacdnae

refdndantur, extantemediautrinq^ fuper alte?

ra diamctro quxapud d defcendit in pede, acci

piamr ex pede diftantia par priori.Eius armil

Ixquodfupra eft elimeturfupermediadiame

tro D procraffitudinearmifigcfimiliufigno^

rum * His omnibus indfionibus coaptaris, ar^

milla F AEjfimulcumfphscraconfixa:ponatur ncifuras apud & s armillac mrsc.Sic utambarum interiores circumferentix

naiiifaciantccquilatadonemadglobuiiijobfer

uetur nc niutetur facies. Verum qux defignata

eftarmilte F AE,refpidatR fignumalterius,

Poft, armilla mds v inferatur in illam mrscfecundum fimilia figna & s, SCconenimt fi*

bifecundum exteriorem fuperfidem.fi quidin

alteraintortueft corrigat, ftabitrurfusarmilla

F ae infuperficieMVSDjUndeexdfafoit.

Fiflurareliqua bafis ab intima circuferentiaad

cofirmetur rurfus 5perindudam tranfuerfam

laminamlongamlatamq? minus digito &confixam.Armillcautem dimidiatae R D C bafis in*

feratui alteri bafi, fic ut duae ftent una fuper^

fide. Interioruero eius ambitus couemat cum

prioribus mrsc,&afb ae in a?quilatatione

ad

C S R V C I . j?

adfph£ram. Capitib.autR Sic inferaturin per*

tufas partes alterius in parib, fignis . His rite itis

ferris^fefeuicifflmmordicus compIedentiKaxis g imponaturarmi%mvs in figno*

fic fineiuo f tendatre&e incentnim,&configatun Fron tes quocpquartarumVR&vcaipudvdrcuddantur in rotundum, ddndefiusaxibus fuipendanturadaxem nuncconfixum,undetanquamexpolo defcendatiiiperfuperfi*

ciem mrsc, experiaturq? utfineuido quaqu&suerfummoueantur. Quodutcautu fuerit,im*mittatur ftridim&coa&ein cauum axis primicu lato &plano capite, utcontegat&contineat

axes quaitammPofthaecdiuidaturquartsearimillarumM vs& R &C v,fuperfumma at<J

mediaipina in partesqusequepro fe xc affinesj

his quaeperearu iuperfideantea digeftac funt*

Canoniumquoq? fiat, quod dirigatlineammcridianam,uidelicetin fuperfitiearmillse r proxime M,fiatcauumrotundum inftariciotherid

compaffi :perhuius tympanicentrumducaturparallela s ,& centro figaturaculeus,

cui fuperincumbatlingulamagnetis nutans adomnempofitionem, &os tympani daudaturctyftallo.Sed&Tper iuperfidembafisiiibtus

defcedat perpendiculum parallelum diametro

V Djiecundumrationemlinesc xy, Hocper*pendiculum corrigetfitum organiad planide

horizotis Hsec efttotius conftrudionisrmot

c Proderit

D S R

proderirautc proponcrccfiigicni opcris den

ia charta,& ea experiri tota concinnarioncm

extraiacfhiram.Nequeenim omnis commodutasfatisdeicribi 5 nequeomnis erroriemel iatis

caueri poteft,

1 D V C I O,

PRimi qui coelitus res ad difciplinam addiu

xerunt,non potueruntinuenta fua explica

refatis , nifi organum coftruxiflentexemplum

coeleftis corporis,quodreferretcirculos cogna*

tos, &CrepradTentaretortuSjOCcafus fiderum,ac*

ceffiones ad climata, &C receffiones, deniq?onunes euentus , quales plurimi ex coeli conuerfio*

ne continguntcircumambitum terrenum. Ers

gopropoiuerunteffidumorganum: quodduplicieffigiepofteritati commendarunt, unain

armillis corporalib. quam uocarunt pertuiam,

alterain cotinuafapcrficieabfolutaepila?. Etha

bet utraquediipofitio eandem potcftatem, Sed

placuit Proclo fphaera corinua, qualcm pridcm

coftruximus , &qua ufosfuifTeueteres probos

autores fatis coftat. Ob perpetuam enim iiiam

faciem,& lineares tenuiflimos circulorum du*

dtus, &coeleftii5imaginum comprehefioncm,

multocognatius euidentiusq? fubindicatcode*

ftis corporis habitudinem* Priorautem forma

armillaris utneceffari]s quidem negociocircu*

lisconfta^ficreliquaipfiusjquiainaiiiafun^au

ferunfc

CONSTR VCTIONI, 7feruntoculiscum craffidemateri^tum ipfa inanimteiliperiorumphantafiam. Fitqpdum drciilos fpharrales tantu uidemus

, requiramus fub*indecorpus qualecircunfcribut Sedhabet hecetiam immenfam utilitatemaliam, quantaiph^ra folida prasftare potefbdequa alio loco rurfus dicemus. adeo alteraalteram pncftat,&neutraalteri ufu conceditVtratamen utamur

5conuenitcondpereanimo rarionem, quapropoii*tumorganu fubfaciemcoeli coponatur. Quocnimmodo umbra a lucefua no recedit, fed huic illafecundum linea reipondet: eomodo fphgraconftru&anon receditab 2ethereafphgra

5fedhuius drculidrculis ilhus,&pattcs partibus

)&:tota toti fuperincumbit, Ergo fiquapoteftas fit

fecfla nobis, fiuequia eafadano fiiitvrefcramus

fakemimaginationecentrum iphaenc ti*

pnem centri terra?, ficquodduo h£ccentrauniiilliceireintelligatur, quomoclo dua? gemmulseroris in unamconfluant. Hacimaginationefuperfides fphara noftra?ambibit centrum uni*uerfi,non fecus atqpfuperfidesfumma terrse,&codum illudambiunt Deniq; ftatuaturillicor

ganu, ficutipfiuslineaM s extendatur interau*ftrum etboream ad canonemmagnetis.Super*ficies autem armilfe r s c planidem horiszonas mundani fecundu diredionem perpen*diculi x v. Hoc fitu organi intelle<fro circu cen*trum mundi, quapcunquepunda, Sc quicunqi

c circuU

D SPftABR At ·

circuli ex coelefti fuperficiein centru perueniut-

quoniamperaenire nifi fabre

fa&se fphaerscinteruentunon

poflunt Sequiturutfadatin

eadefignationes rjfdemnominib.&rationib.quibus in cce

lo cenfenrur.Eftoenimambo

bus ccelo &fph^rac commui

necentrum e>&C portio cardi*

nisinterid&rmeridie pertin*

gens ,porrio cceleftisam«

bitus N.Sphaerarautemnos

ftra» , Ggneturincoeto quodlibetpun&um,

ut c, undeperueniatreitain centrum . Secat \U

neain , fpherad pundum fimilis rationisdinccelo.utcparcusM c5

itaarcus D,quiauter^

uni angulo iubtenditur, itapunda pucfHs,

circunferentiacircunferenti^& tota fphaerato

ti ccelorefpondet^edputabitquilpiam obfta*

rehuicailumpdoni^quia ftatuere fphaerain cen

tro untuerfi non poffumus ,proptereaq? relatiV

defignationes afemutuo diffidebuntvquan

tum diftant centraamborumfph^ne&uniuer

fi, Refpodemus, hocnopolTeinfirmareailum

ptione.Habentquidem terracfumma diftanria

memorabile h centro.Sed ubi terra tota adcodi

fpatiacoferimus ,idquodnoftro fieri negocio

oportet,totaquarta a centro aflurgi^ukem nifi

pucli tenet, qa manifeftis experimetis alio loco

ofteru

COKSTRVCTl ' . fr

oftendet,&nucutreceptu uolumus.Ergo redi

mus adaffumptionenoftrajfi^deinceps tra&a

mus iphgra hancin terr^iuperficiepro cocleftis

etiuperficiei experimetocaptando,omnes lineg

circuli intelledi egredi ex cetro organi perquafe

cunqpipfius {e(ihOnes5pemeniutre&ain iuper*

ficiecoeleftiineiufdemnotsecirculos &*nes. Poftea,fiquaeProduscoeIeftium fegmen*

torum definierit,nos ih fphseraexemplari

defignabimus,id quamuis in altero

fiat, tamen in utrocp dcfigna*

tum accipi debebit*

c

Sft>{/,$ /* cdir>%

KtyovT^ 7tf-*&jj^ &*

yvnu.^, <fi.&, </j&@^^ 7&/ -. :

jocfj$>«^7& .&- ySLv- TQf\ u$^ * wccf *>«*\& ivcu. «^ Svou. ngu, hi twi

yusj7rtf* «< &*PROCLI DIADOCHI SPHAERA,

LINACRO R I

1NTERPRETE.Oeaxi &polis»

Xis mundi uocatur dimericns ipfius,

drcaqua uoluitur. Axis extreina,poli

mudi feu u^rrices fun t nominati.Ho*rum alter feptetrionalis, alterauftrinus dicitur.

Septentrionalis,qui femperin noftra habitatio

neapparet.Auftrinus contra5quifemper5 utad

noftrum horizonta,conditur,Suntautein ter*

raloca qua?da\in quibus polus5qui femperno*

bis coipicuus eft,r)s qui ibi degun t haudquacpcernit. Qui ueronobis perpetuo occultus eft,

rjfdemcofpicuuscuadit. Rurfus quocplocumquepia in terris inuenias,ubiambo poli aequas

bilem in horizontefitum habenr,

S L I ,

Ar

S C L I .AwV.) Axis mundi eft ut linea tranfmiffaimaginarkper fpharam.

hmusamfummafignafunt A B, & quidemBpolusborealis,Aaufiralit^

ln noflra.) Nojira habitatlo eji ab Aethiopum climate pertinens in bore»

4tn, at(p is eft primusfitusfpbaree ex tribus quos Proclus explicat . 1 ta autemreprafentatur,AE fignumfubaquinottiakmoueturexuerticeV uerftts M,framdumquam libuerit dtflantiam . Hoc fitu polus continuc Uuatur*pra horizpmem & huiusftgnum S, undefemper apparet. Sunt tamen.)

U ejlalterfuusfphxra, quem habentloca ultrddima Acthiopm uerfusau

firum^ualia repcrerunthac atatc Rifpam . Ita autem deftgnatur, AE fignii

moueturex Vucrticeuerfus s horizonth perquamlibuemdiflantiam.Hoc

fuu polus defcenditfub horizpntem apudfignum S. uero auflralis coru

fpicuusfiet, leuatusfupra hori^ontem apud ftgnum. Kurfus.) U efi ter

tiusfitus fphara, qnem habent loea media ethiopum,funt'<pfukperpencb

cubaquinoftidtis. ltadUtemdefignatur,AK fignumrepomturfub V uerth

cem.uocfrtu mudi,polui uterqj & Btconfp\citur vn plano horiqontis apuds& M.ufitusfphxra dkitur refius,priom obliqulHacforfan mamfcftio»ra cuipiam uidentur, quam ut extra autorem debuerint fmgulariter enand*n.Scdcoucmttutficut Proclus ex his initijs, nulli ignoratafunt, alia du

cugrdulorajicmiadfcquentiumfphteralmm mumojien[ione,ab hocor*

dmeUgttimeueniYcmm. (*TvyF 7w o-cpcufCL «V/§<79,

tofoi>ot 3</1&.·,/^&.&-

jj-^^ ^^

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vpoTrbh&.£« pS& \*& vvfW/TtA«7f &.$>\& V&v &*givlw^^ & ^wuyJSgtxy(/14\^^/,' u$ ,&^*. )^.[\ #h y&i^ [^ kj &(£>( *\35> yny >>&otsqtoy cjfgc\ tfeiy §toj>x[x*

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<£ & , &£9* *^srgiof/·> ty*»^,) \(* ycty W**& &. $ &~ QmgwL

D CIRCVLIS SPHAERAE,

Clrculorum fphsefccalrj paralleli funt, fiuc

equidiftates 5alrj obliquijali) perpolos du

&iAequidiftantes funt,quibus rjdecummundo poli funt , Suntaute hinumero quinq? : Se*

ptentrionaliSjSolftitialiSjAequato^Brumalis,

Antar&icus. Septentrionalis igiturcirculus eft

isjquiomnium^uos perpetuo cernimuspla-

ne maximus eft, qiriq? horizontefolo pundocontingi^

contingit, totus iupraterram intcrccptus. Inter

huncquaxunqueciaudunturaftra, nec ortumnecoccafum norunt, fedcircapolumuerti tos

ta no&ecernuntur. Porro is circulus in noftro

tra&iijapriorimaiorisurfepede deicribit. SoUftitialis autem circulus is eft, quiomnium qui a

ible deicribunturmaxime ieptentrionalishabe

tur? Inquemcumie folreceperit, seftiuam reci*

procationempera^t, longiffimusq? totiusam

ni dies> breuiffimaq?nox erit, Poftaute rccipro

cattonemnequaqua ultrauerius ieptentriones

iblemprogredi, qui potiusad diuerfamundi re

fedi cernas : unde 8>C tropico grsece nomen,quatorcirculuseftis ,qui maximus a?quidi=s

ftantium circulorumftatuitur, ita nimirumabhorizontedii!echis,utdus femicirculus fupra

terram, atter iub terracondatur , In hocfol du*

plex scquinodlium, uernum,autarnnaleq?faak

Brumalis circulus is eft, qufomnium circuloru

qui afolecircumadunudi deicribuntur, maxi^

meadauftrum pertinettin quo folbrumalem re

dprocationemfacit,maximacp totius anni ,minimustp dies efficitur. Pofthanc metam ne^

quaqua ultraprogredit ibl , fedad alteras muiis

di partesreuerritur; undetropicus hic quoquequafi uerfilis appellat. Antar&icus uero circu

lus, sequalis &a:quidiftans ieptentrionalicircu

lo eft,&Chorizotauno con ringens.To*

tus prartereaiub terris mcrfus5intra quein fita a*

«fi, d ftra

<?

ftrafempernobis occulta manet.Maximus au^

tem ex quinquememoratis circulis eftaequatoiy

deinde tropici.Miriimi uerb(quodadnoftram

habitationem dixerim)ar(flici. Porrb hos circu

los, citraomnem latitudinemintelligi couenit,

rationc cognobiles ex aftroru fnu ,& eode dio*

ptr£obtutu,&noftro ntelle&u delineatos.Sen

fu enim unus lafteus difcerni in codo poteft>re«

liqui omnes ratione*

^ S C O L I A,

0Mi$«i.) Vr eftcirculus CGDH, de<jHo pojieriui dicetur. Aequis

Apantes.) sumptoarcinopes eiuidlterfldtudturm mc/ polumy aU

icrextenddturadaliquamdiftantidmabaqudtore CEDF; auem ficdefcrh

hlcircumfpharamcontingetjicimuscequidiflantem, Eiusgeneristantum

quknp dffumpfit Proclm, fidles defcrtbi contingu perfignd cr ex

,-per G &S ex ,' F expolo dlterittro. Septentrwndlis.)

Stdtudtur AE fignumdd qudmlibetdiftdntidmex V uerttce uerfus ko;

j^onm,&prrrirani/fatM4fwm pohim , d/fer exfenc&ift<r ii) S confds

{ium horizontis fph<srce% cum ed extenfione defcribi intelligdtur circulus

perfpharl: h eftfeptenmondltsfecundu omnem conditionem Procli defcris

ptionis. intrd hunc.') Sk ntdgisproprie dixerimus quam in hoc,ut uulga

taexemplarld legunt.lntrd ht^ic,ncptfeptentriondle. igiturfignetur auod=

libet punftum fuperfphard propius dd , quamfn S fignum , uoiude

turfphcerdinfidrmotusdiumi. idempunflumdppdret femper leudtumtos

tdconuerfionefuprdhoriKontem . Emsckculirecentiores nuUam fdclunt

tnenttonem: ueteret uerb pracipudm rationem hdbuerunt . Mfmimt huius

Strdbo proxime inhium operhdefitu orbis: uerbd eiusfiint ex caly Cdlcds

gnlni trdduftione. Qubd autem ad urfds extrcmitds dttigud fit ocedno Jic

innuit de urfd loquem: Solaip ddocedtii declmat bdlned mtnquam . Per ure

fam entm o-plduftrum, drftkumfigmficdt. Ne<penim auom tot Jleila eo la

co circunferantur.fcmper perfpicuo foldtn dixh bdlneorum expertem oceda

m,ne<p adeb eius imperhtireddrguum,qudfi umm urfdtn pro dudbus dgno

uerlt; necp cmtn confentdneutn erdt, nondum dlterdmm ajirddfcitdtn. Sed

ex auo Phcenhes notdriit, ttfifunt ddnauigdtionem, huncquo'<p ordinem

ad Gracos perueniffcftcut& Biremces crimm ©· cdnopu heri& mdmster

tius denotnindtii: multdsip dd hdnc ufip atdtem ftne nomine mdnere, ut etid

ait Ardtus. tionigw ttftefcribit aratts;Sokmemtxptrs eji balneom-,

. .. nonfugm

* . - *tionfugknddfugiem. comodior HerdclitustO- Homeroapttorjtmittterpromilico urfam dppellis. Auroraenim& uefpera termini drftostidefi>urfd.

Ef contra,urfeterrmmsferem louU. Artticus enim occafus t? ortus termi

msefi,nonurfd. Perurfdmquidem.qudmo-pldufiriiuocdt, o- Orioneob*

feruare dicit, drtticu mtelligit. Per ocedniidutem hori%ontemt tn quem, o*tx quo occafus ©· ortusfiunt. Dicens aut ipfum uerti cexpertem ejfe oceda

mt nouifje cognofchur qubd ddfignu mdxtme drfticii hori^oth efi drtticus.

Confequeteritd<p huicpoeticu illuddccomoddntes, horizontemquidemdes

bemus dccipere, qubd terra ulcmii eft ocedno : drflicumdutm, qubdtenxttttiguum, qudftfignit hdbitdta pdrtismdxime drflicum fecundumfenfum:qudre hdnc terrapdrtem ocedms dlluit. Hdftenus Strdbo, er uerboriiiU

liusferekxceflfententid. Cumeniminhocfufermone, utdfjerdtoceanum

circunfundi ubi<$ terris, ne cui qubdddfeptentrione quoqj circunfunddtur,

m dubium ueniat, conjimdtfementidm cdrmne Homerl : Soldcp ddocedni

declinat bdlned nunqudm. Cuiusfubmdefenfum endrr<is,inquk,Poctdm lo

de urfd tndiofi . Per edtn dutemfignificdre circuti drfticum , per ocednii

dutem hori%ontem, infrdquem drtticus non defcendit ; ficqj uerbis dcconis

moddttsfuo drgumento,fupremdfententidm mfert ddmodum hunc. Poeta

nonfuerh ufuruswmine oceani pro horiqonte hic , ubi non occidere urfdtn

iixlty nifi illic ejfe ocednum mtellexiflet . igituv ejl ocedtms cum dlijs mundipdrtib. tumhocetiamcdrdinefeptentriondlicircunfluus terrh. Hacfum*mdfententid efi , nunc uerbd eius loci pdrthuldtim expendamus. Nequeenimcum tot. ) Strdboexponensurfdmprodrfiico,nefdcerecodfliMuided

tur cdufdm fuifenfus, rcdditm modum hunc Poctd, dicens: Solddd ocedni

declkidt bdlned nunqudm. non potult intelligerefoldtn, nempe urfdtn exper

ttmocedm: tot pratereafiellis m eodem trdty cali expembus ocedni.

• Ne$ ddeb.) Duafunt urfie: mdior,qua Cynofurd: mino^qua Elice; hdc

Gr#ci, illd Phcenices funt ufi in namgdtionib . quod Ouidius tefiaturm F<fs

/?ix: Kffe duas drttos,qudrum Cynofurd petdtur Stdonijs, Elicen Qrdtd ca

rind notdt. Elice proximd uerticimundh immb qui polus uocdtur extftit

inillius,'^* boredlib. longeeldtlor fuprd horU

spntem,dcinde Gracis notiffimdJoUd} obferudtd in marl obquds res pof*

fttquifpidm (quodo Crdtcsfdch)fufpicdri,Homeriiedm pracipuenotdffe

illocdrmine ; alterdm uerbficutiperegrmanedj nouijfe . Hocrefellit Strdbo

vkquienr.Nemo reddrguk Homeru eitts tmpernia, ut und tdntu urfdm noue

rit,cum dua fmt, neip quifpidm drbitrdtur Cynofurdm nondu peruenifle >*

tdteEomeYidddracos immbexquotemporePhanicesedm obferudrunt,

ipfdh Greech etid celeriter cogmtdfuh , quomodo atdte nojkd Berenich cri

ms,c cdnopusftelLe dnnotdta heri mdtus tertius db Aegyptiji : ddGmcosquo^fere perendie peruenerut.Sic Strdbofdthfdcit pro dfjumptd expofi

tione* Mnltds^.^Ne alitnu ijlud uideatur,nouds dtnicp fielUs drmotariM*

d t quitfdUz

:auit, autoreetUm Ardto chato in teflem,hdudqudd.udm omnes annumtra-

tns hatlcnus ejfejmmb reflare adhanc ufque atatemmultdsfine nomne&i

cbferuatione. Aurora& uefpera. ) Denotat hominibus ipfos ortus

occafitsftderum perukcs, «p cefjam effe m ciradodrtlko, ut Proclus mes

morat,v nos in organofphtra ofiendimus:U uMcetjer non urfa pro;

mhtrmmtfereni \ouis,fiuc*iaora&uefpera. Quodurfaautceffeeius

tcrmirvas diatur, hoc adeb , csubd hwus nomine Romerus utkur prodr,

dico. orionem obferuare dicit. ) Qwif hodie «fierifmus uocetur Orion,

uulgdtius ut conucniat ddmonere : ucmm is difiat db urfd mdiorc

perfuperficiemcali pdrtibusnonmhws Ix. circulimdximi t<{ua dtfianM

fdc\t,ut dchocdfierifmo loaui Eomerus non potuerit, qudfi hunc urfd obfer

uet. Sed Bootes dicitur cuftos urfaunde ilh Artiophylaci nome. Et hunc

ejfe ditium plerifp orionem, dutor Hefychius in ciilione:^*. a*p2pomnsoy0/ua{waifio0T(ut: idep,Orion>confiitutioex xxiiij.fieU

Us,<ptemnonmlUdppeUdntBootem. Exhwusdutoritdtc fentioHomtrum

fuborionismentionedixijfeEootem. Adfignum.) Mdximedraicum,

id^ urfdtn uerti effe expertem ocednhintcllexhftgmnon quod*

Ubet horizotis , fedquod ipfius eflmdxtme boredU, utpottaucd nos infph*

td oftendimus effe in communi contdftu e;«r, & drtiia dpuds figmm.

Confequenter. ) ^^^ ^°'^ 0<:€0 ^

horizonte dhimusfecundum caleftemfuperjiciem. sed hxc ut ddtenenam

accommodemus, dicimus horizontem debere dccipi m tmd figrmm, oce<u

nodttiguum.Arfticumutrbftgmmt^udeiushdbhdta^

boream dccedit. Perobfcuredutem inmitfubuertkdlUpunfld,!? fubuers

tlcdles circulos, qui in terrd defignantur ex perpendiculo fimilium m calo:

tdquodmgeogrdphicistrddifiombusopportumusdecldrdtur, Poftlongdm

dijjertdtionem Strdboredtt ddcceptum initiofermonem concludem: ftdre

O-hdncterriepdrtemocedtwsdllutt . Verumnospropter unius drfticicir*

culimemwnem dd hdnc uenimus longdtn digrejfionem. Porrb is circu*

lus. ) Stelk d priori pede mdioris urfadefcribitur , rddtcem hdbet dd

atdtemhipparchi grddus xl Umutids primas v. cdncri .Ldtitudimmdb

tcUptkaborealegradusxvij.. M. primds xv.fecundaqudmrddicemfiinfcri

bitur mfpharam :mW eim rdtw pojlerius trddetur ,reperitur declmdtio

dbtqudtoregraduumarcher xxxh. Leueturergo hpolusfecundumtotu

demgradusfupra S horiKontisyc\rculu^driiicmperhdncdt[tdnnd 6 3

duci intelligdtur clrcumfuperficiemfphara: qwftc duflus fuerit , ibit per

medidmdnnotdtdmflelldm,dtqueidemdrHkuuenfetwfecundumd^

ptum Procli climd. Kceccdufdfuit Homero , ut uteretur prcmifcue urfdpro

drflico. Siquidem fub fuo \llmsc\imdtecumdrtt\cm cfrculusper pdrtem

urfa rdnfitttum urfdpdrtefui drtlkudefigndt in chmdte^uo is edtn obftt

mwnefpharafcribdaMUodfercdccidit tm*Mtu*,tt urbiAthendnu

Solftitialu*.

> ,:

SolftUlalis.y idefiquiexB ,-extenfioneE G ptrfphdramdefcrU

ptusefl. Longifjimus.) stdtudtur jphxrddddflumpMpriusclimdAthe*

narum,solfiicialis pdrtemfuaareunferentiitmaionm habetfupra horizon

tem. Per quantam ergo portionem cttmfol defertur, prolixius curfum confi»

c\i,quhm aliquo alio ecliptica loco uicinwre aqudtori ; rurfus noiie celerius

perficit, cjuhmfub aliquo alio parallelo, quonidm partem fui omnm reliquoa

rum brewffimam habetfub hbri%onte. AequatorS) U f/, qui ex alterutro

polo fcribuur medtusfphara, ut circulus CBDF. Brwmd/w.)

lf efl qui ex polo, & extenfione defcriptus efl. Antdrfticus.) Si<fc

tuatur ciranus in polum, pts etus alterextendatur in cota&um fphara cr

horizontis apud ftgnum, circulusqui indrdefcribikiteUighurperfpha?»

ram dicitur dntdrfthus,eequidijidns reliquis memoratis. Tamen feptentrios

ndliaquidifldredtcituraProclo, quontamduohicx pdriconftant aquiUtaa

tione. Porrb hos.) Sdtis liquet exprafentutm defignatloutaequidiflantes

memomtos, & omnes circulos caltjies carere latitudme, effeip pertenues li

neds.Porrbinfuperficie caleftitne<p'tfiudhdbentqubdforet ddeummodum

tndmfefi,fedquomodofemttam monfiramusm dere uohtcris prteteruolan»

iisjmb quomodopdubdnte drflicos imagmdrios delmeautmus perfphara:

eo modo quosltbet circulos infuperficie cali defimmus phatdfid,exfidto tr<m

fitu dfirorumfub conuerfione diurna. Ex aflrorum. ) Afirorum fuus

locus cuiufquefuusin dxfidiitia ctxid exdhquo afjumpto punfio * Sicut quod

orion ejlditfirdlis d uertice, urfd dutem boredlis,qudltsfuus certe oculis de*

prehenditur. Dtoptrcc.) Dioptrdeftregutduiforid,plurimdpdrs'mobftr

udtwnibuidjlronomicisAnhocuerO orgdnoaculeusere&us in fummdfpit

nd,quddrdnt\s habet iocum© ufum dioptra , ut dc ipfms rationc

loco rurfus dicemuu»

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CVR QVINQ:VE V V ·

diftdntes fphar*.

QVinq? uero dutaxatsequidiftantes circu*

li defcribi in fphserafolent,quod tame

eo ualet,quaii hi folrinmudo aequidiftates fint;

quippecum ibl quotidie ccquidiftantem ^qua^

tori circulUjquodfenilxanimaduern lket,mundi rotatu peragat,quo fit ut intra circulos tropi

cos centum lxxx.bis circuli paralleli a fole defcri

bantur » Totidemenim dies intrareciprocatioi

nes numerantur. Quin &ftellaeuniueriadn ae*

quidiftantibus circulis quotidieferuntur, nontamen hi omnes in fphseram adhibetur.Quod

tametfi mulrisalfjsrebusin aftrologia condu*

cancfiquidem fieri nequit, ut.uel aftraprobe in

fphaera

* .31

ipharralocetur fine omnibus sequidiftantibus

circulis, uelexamuffim dierum nodiumqpma*gnitudines finerjfdeminueniantur:tamequodadprimaaftrologiserudimentanonadeb utiles

exiftimati iunt,paruuifumeft eosin iphaeram

afcribi.Quincpuero a?quidiftatesdrculi ob cer

tacompeiidia, quacaftrologice tyronibus affes

runt, optimoiurein iph^ramfuntadhibiUSe^ptentrionalis enim, aftra quaenobis perpetuocernuntur definit, folftitialis tropicus folis red*

procationem continet}finisq? efteiufdem in bo

rea tranfitus, ^quatordrculus aequino&iacomplc&it. Brumalistropicus folis ad auftrupro*

greffi meta eft,etbrumaledus redprocationeminfehabet Antar&icus drculus^ftraquamo*

fliTimcofpedumfugiutdeten^inat. Itaq?cumhis quiprimis aftrologisc rudimentis imbuensdi funt,certa emolumentafliggerant, merito irt

fphaeramconie&as quis duhmuS C L ! A.

Quodtamen.') Locdtoeritmfolefubquocunajpunfioecltptice C CT>Jf9tum co loco exiflem , cbcuferdtur perfufnficum cali conuerftone diurna,

xntellignur ex illo puHo defignare aquidtflantem eo exemplo,quo exifiensmalterutrofigno G uel ujeftgnat cequidijiantem aui trcpicus dicitur. qwofit .) Uenda in numcro. Bis envm c xciij. factt ccclxxxitij . quot dks in arts

,-integraln eclipticdpunfianonfunt: legendum fuerit clxxxy . Secuns

dum enim dies anni tteteres adnotarunt, aqiddiflantes aquatorifatis probda

hili ratione, qubd totidem dies intra reciprocationes numerdntur » Medieta»

tem autemdffumpferunt, quonidmaudnto numtro dierum trdnfit d tropico

in brumd , tdnto redit k brumadd folflitium . \ntelteflus eji dutem fol defu

gnare,diebusfingidtsfingulos pdrdllelosaqudtorimflar fummorum duoz

tiiMtduifumddfolftitmm&brumdmsxG figmsduftiperdmbitum.

Quin &fielU.) signftur enimquocunas hcofpbarawnttum tanqudm

[tclk

j*

flelld foret, tlludfphara reuoluta intelbgnur defcribere,»curAurMioncmqualemdefolcnmcdmmus. Siquidem.') quomodoftel

U infcribantur \nfphicram, at$ magnitudines dierum nofliwro exaquidi

ftmihui deprehendatur,f>oflcrius dicemus»

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DE OCCVLTATIONB Rs

fu (equidiftamium.

Erumex memoratis quincp equidiftatib*

V GirculiSj arciicus iane fupra tefra totus exi

ftitSolftitialis auttropicus5biparritoabhorizo

tefcind&maioredus partefapraterram conipicua, minorefubterocculta. Neqptamein omnitradujurbeueiimiliterdrculus hicab horizonte fecatur, fedprodimatum uarietate,uariam fe*

ctionu exuperantia forritur: rjs quoqp,qui pro*pius feptentriones agunt, in^quabilius ab horizonte icinditun Nec finis, donec eo loci ucntufit, ubi totusfupraterram emineat.Qui ueroadauftrumagis uergunt, rjs profecftoper inaxjua*

biliores partes ab horizote diuiditur , don ecadplagam quandam uentu fit(nobis certe auftra**··· - e km)in

14

iem)inquatroptcus ab horfzonte peracquas

partes fecatur.At in noftra habitatione3itafol(ti

tialis ab horizontefdnditur, utuniuerib drcu^

10 per 0A0 partes diiTedo, quinCpfupra terram

appareant, tres fub terra lateant Sanead hoc di

ma direxiffe ftilum Aratus uidetur , cum Phass

nomenacofcnberet, in quibus cum de folftiria^

11 tropico difTerit, itaait:

Huius in o&onis difledi parribus, alta

Terraru inuifunt quinq?, tres imafrcquentant

Alterni& Phoebi reditus celebrantureodem.

Exhacdiuifionefequiturmaximu dkmhosrarum equinoctialium quindedm efle,no(f}:em

uero nouem. In Rhodio autemhorizote ifa tro

picus ab horizonte dirimitur , ut cumcirculus

uniuerfusinocflo& quadraginta parteis fecet,

undetriginta iediones iupra horizontem appa

reant, undeuiginti fub terralateant Ex quaduuiftone fit, utapud. Rhodios longiffimus dies,

horas ^quinocfhales quatuordecim habeat,nox

nouem, additis hincindefemiffibus uniushos

ra? fingulis.&quatoruero drculus, peruniuer*

fumterrarumorbemita abhorizote diuiditur,

ut femicirculus dus fupra terra extet, fcmidrcus

lus fub terralinquat Quo fit , ut in hoc drculo

aequino&ia fiant. Brumalis aut tropicus ea ras

tioeab horizoteinterfaflus eft,utminoreie(fHo

nib. fupra tcrrahabeamr, maior iub terra. Ina?s

quabilicas uero fe&ionueandemin omnib, di*

matibus

2 » lf

maribus uarietatehabet, quam etia iblftitiaH

tropicodiximus. Semg enimreipondentesexaduerib tropicoru feftioes^quales interfefun t.

Eoq? fit,utmaximus diesmaximaenofti, &Cminimus diesminimasnodisequalis euadat An*tardicusautcirculus totus fub horizontelatetv

S C O L I A»Ne<ptdtnen.) Ltueturenim Bpolusfupra s horizontis per punfld, uts

pote xxx. solflitialismaiorisfuipdrteemfuprahori^ontem, leuetur palus altiusjotfittidlis item dmplioriadhucfui portione quimfuerat, primuttritfupra hori%ontem, hoccpillicontinueaccidit magh, quo magis leuatur

polus.Sic tdndemeueniet,ubi polusitalcuabitur 3 ut circulus duflustx L ueneritfub V uert\cem,qubd folfiuialiscontmget hori^ontemapudS, totusergo dpparebit. qpi uero. ) Videlicet populi qui mdgis dd dusfkum concedunt,qum hiquorum tmncfitumfphara exhibuimus hist er,nrgocouertdmusfuperiordexempld

to- B polumdimouedmuscontimtemdgtsh uffike: eritquodsfolfiitidhspdrte fuidppdrenteaqitdbilior, continue

ti non dppdrenti. Donec dd. ) EdpUgd efi fubaquinottidlis , fiue fuusfphararetta. Oemutdturhddj polusufipin S bori^ontis, uidebiturfoU

fiitidlis pdrtib.fuis cequis eflefuprdfubtu/dj horizontem . Ex hdc dimfio=

ne. ) solfiitidlis intelligitur diuidi mfidr aquinoftidltsm punftd ccclx. qu<t

fimultiplicenturin y. pdrtes: uidelicet folflitidlisdppdrentis, o-fummd di

utddturper viij. totdmemscircuferentiam^roueniuntpunfld ccxxv.Kacdmiddnturperxv.undtn uidelicet hordm aqudlem,proueniunt horee diei maximi xv. Notfem.) Secundum priorem rdtionem pdrtes tres non dppdx

rmisfolflitidlisrefpondentpunftis cxxxy. Hxcreddunthords aqudlesix.

Hac qudntitds dieimdxim ©· nottismimma accidit m chmdte Athetidrii:

quemfuum reprafentdmus kfpk*rdy ut AE fignum dimoueamus ex uer

ticeuerfus M,perpdrtescirc'tterxl. Q-femis. InRhodio dutemhori^ons

te.) Suffecertt prius explicdtum exemplum,pro hoc quoque loco exponeris

do. Pofierius tdtnen cdnon ddbitur in uriiuerfum, quomodomaximm dies ex

dato climdte,uictffm cltmd ex dato tndximo die deprehenddtur. Brumdslis. ) H*c hdbitudo manifefld efiexfuperius endrrdtis, excp mfpettioefpha

r*:qu4retwll4cdufdeft,utcircaeamquo<poccupemut.

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vovTxt*& cftt<& 7r&g ctfK&y{$# , fi\

woA9j KOLrie yit/iTXi . $ rfw&& rtxpy^ ^6)-,& &'^£&%~9,csv f>&$2, "Toy ikgKTiKoy£ ^yio-Hyi^ivoy^i^. y^y*\ov\x -€^> >7&-'^/&, £ nrotei7{ ywovTTtiji j. ngu % 7&*<THy€ft<xy^&&&*< Xby K^yoykin \z®v \^ « y$j/ \zsro rvy^ yivov) ccg-

/9*( CU>CUQ0U2)T? , CWTI 'gxThnKtoy«)/^«? ym^j, %3(ga^y lo-vy-^ivQy*

D MAGNITVDINE Q.VI DI ST VM.

SEd ex quinqp iammemoratis drculis, quo^rundammagnitudinem, peruniuerium ter

raruorbemeade fibi conftant^nonnulloruprodimatibus mutanturjalrjs^maioreSjalfjsminorcscirculieuadut,Tropicienim &^quatorpas

res per totum orbemmagnitudines feruantAr

» |7

fticimagnitudineeuariant,cum alibi maiorcs,

alibi minores cernantur.Quippehis qui fepteri

triones uerfus degunt, maiores ieptentrionales

fiunt, cumpolomagisinaltumfiiblato arAicucirculum,qui horizontacotingit

5neceffe fit affi

duemaiorem ficri.His uero qui magis etiam adfeptentriones uergunt,interdum folftitialis tro*

picus ardicum plane abit , fitq$utduo drcusli ieptentrionalis, tropicusq? coeant, pro unoq?habeantur, adeo cu magis adieptentriones etia

accediuir,maiores folftiriali tropico feptemonales redduntunNec finis donec eo uentu fit:ubiquoniampolus iixpra uerticem conipiatur

,

ptentrionalisinhorizontislocum cedit5 dq? in

mundi rotatu coiungitur}a?quatoris planemas

gnitudine,fitqp ut tres drculi3feptentrionaIis53c=

quatorethorizon}eundenifitiipofitum9obti

neant . Rurfusautcm his qui adauftrum habistantpolihumiliores fiunt, feptentrionales uerocircuiirninores. Finis aut decrementi, eftlocus

adauftru nobis fub axjuatore, in quo poli fubhorizontehabetur , Septentrionales autem cir*

culiprorfus euanuere:ita ex quinc^asquidiftan

tibus tres deniq?fuperant5nempecum acquato*

re,tropidduo.

5 C O L 1 A,

Cttm polo.) Oiximustoties circulum artticum defcrihi ex pobt&ctis

fiamia ad s fignum korizoMh.Sequkur,ut quoeleitdtiorefipolus,eo fttnut

St &m4iorcirculurf<imexm4Mridefa^ *

~~ - c j nk

,a

Bif uero.) Admoueaturfphara \n L punflofub V uerticem,c\rculut tx

S iijidnuddefi^dtusprodr^tcOtidemmciditinipfum folflitialemt eft$

u pro ardico. Adeocum.) Admoueatur polusuerfus V ucrttceprot

pms fttupriori drcus S,euddit dtnplior ddhuc proximo priore .IgituretH

arfticus s rKdiff nwc nwior priori folflitiali. Necfinis. ) Admoueatur

/w£> V ucrticcm,o-ipfo exemplo euenient, quahic memorat Proclus: nift

quodno tres modofedomninoqudtuor(ndmtribusddditurdntdrfticu:)eun

demfttumhdbent. Rurftu autem.) whduidddufirumhdbitdnt.Xntelhge

non qui ultra aaudtoremfcd <\m hdbitdnt duflrdbord his,de quibus modo di

ilumfuk. In poii.) Sub horizpnte hdbentur,uideltcet mciduntpdmtcrmfuperficicmhorizoMisdpudilliusfignd MffS.£^.

y&f 7>&9 ovxy&oKHrftoy yt*

vi&KC Tzwri7§\ ,\' 7&

-iy \&$).&· &^]>& yivotfxt,^ - ufii

y»s, & , $>

-moAtay^tTH &iy-, vsrfcg ^/*, 7ifO<rctyo%fboy$lJrti -^sro -rvy.DE V R Q.V IDISTANTIVM*

ob ea quscdi&a funt, quinque

perpetuos a?quidiftantes exiftimandum,

led pro no ftra habitarionenumerum eoru exis

fcere; quippequibufdam ih horizontibus, tres

duntaxat scquidiftantes inuenias.SuntianeS£

fupra terra habitatioes ,quaru prima eft in qua

folititialis circulus horizontacotingitjetpro ar

ctico planehabetur fecuda,quam fub polo ap«

pellat. Tertia,dequa paulo anteretulimus, qua

fub aequatorenominant

» 39

o&j/& *r&y 7&> «

•ararga:- <&, 7? ^^

^&^<!·>&'*j7° &, \9^ §<^ ^ fivrtfos ^ 6-) niroi^Tos Aj><>(&&£%&«, yfy ©-& ytvtf

DE ORDINB AE^VIDISTANTI VM.

QVo circa,necordo quincp sequidiftaiititt

circulorum idemapudomneseft,fed in

noftro tradiiprimu fane feptetrionalemdixe*

risjfecundum folftitialem, tertium aequatorem,

quarmmbrumaleni5quinmmantardicum.At

his qui propius quamnos jTeptentriones inco*

lunt,primusinterdu folftitialistropicus numeratur, fecundus feptentrionalis , tertius a^qua*

tor, quartus antarcfticus, quintus brumalis cirs

culus,Cumnanc^feptcntrionalisfolftitialica*

patioreuaditjnecejTeeft memoratum ordinemferuari,

S O L I A,

^SummafenttntUefl, intercircidotattkum&folliuUlemfa&dcolU:

thne,alter altero cenfetur, amplitudmefuperat . Uuenh autequodarHicifint minoresfolflttialijonec uerfusfeptemriones perueniatur adfitu.

fpharaeum^o folfitialis totus tmtrgt&ftt ideyui arfiicus.Etfi polus

4» 6 ·proptus hocfitu ddutrtlcem admoueatur. ipfe quocp drflkttsjit matorfolfiU

,- numeratur proximus ab aqwitore. Exempla horu prius exhibttajunu

sV1 'cct <(& ^,7&.^

k\toy ou. oujtou. &o-iy. yoy> «$>"}>9?,> & ©* yiwroti.o j7^;, »7 yivvmt4J>07TtKQS* Toh Toy·<) &<<

dtftvot &<ri]>. yzs ycty 7*t/loy& k&vtvu.th 7&«9/$ ^xTiixyn

txy $$ -. ol

<.·{ yofy ocy 7&'oivxyS^tjy hgivog \zsx\)(iy-fi ^*

s» ?i- wa^etfj/,W ny ou.Tixy vsrr -^*voy ^^ yivvq -^. yccp*>7 ffl iogvcplw ylvvTta »,· yivov

coJ&h htcu/tw ·§<9 >- c/ji*% . yoty ?9, friyo*. \%rb £\.

D POTESTATE AEQ.V1D1STANTI VM.

IAm uero nec po:eftates , eorundem ccquidu

ftantium eacdem . Nam qui nobis folftitialis

circulus habet,Antipodibus certebrumalis effi

citur,contra qui illis iblftitialis eft,nobisbruma

lis reddit-Sed qui fub aequatore degut, his uni*

uerfi tres circuli uiribus plane folftitiales funt,

utpotefub ipfam folis orbita incoleribus 5quan

quam ad fe inutce conferantur5qui nobis pro

scquatore ftaruitur, iblftitialis uice obtinct.Ambouero tropicipro brumalibusccnfenf. Nan^

qucis demum namrafolftitialis drculus perpe*

tuaq^

\

» 4*

pemacprationem toto terraru orbe dici poteft,

qui proxime habitationem habetur,Quo fit,ut

rjs5qui fub acquatoreagut,scquatoripfepro foU

ftitiali ftatuatur , utpotein quo fol iiipra uertice

agitur.Proaequatoribusautemomnes a?qu duftates drculi,uelutperaequas partes ab horizon

tediiTedi,

S C L I »Solfiitialcm circulum , uocat Proclus omnem aquidifiantm aquatdri

tnedium inter duoi tropicos:in quofolad diem exiflens,mcedtt per uerticem

fubiefta regwnls, utqui per imtium tauri parallelus ducitur , foljiltiahs

habttantib. Meroen mfulam. sicuocemfolfihialisueteresacceperut^uem

illorum ufum qui non aduenunt, nonfacile explicabtmt locum Lucani: Ra*

tidup leonhfolfiitiale caput. Antipodibus.) Antipodes dixit Itberius eos

habitanteseregione&ddauflrumtantum abfunt^uantum nos adfeptens

trionem ab aquatore , Antaciproprie diciirttur : quibtts tandem qul Prs

ticecifitnt, ijdem nobh uere Antipodes extfiunt. Nancp demum. ) Hacrd

tlonequipercancri iriuwmparallelusducitur, Idemcenjetur folflitialis du

pltci ratione: Superiori.quia imtmnet his qui Syenem,at<p periacis qui

idem cUma circuhabitant. Oeinde hac peculiari^uia regiomb. borealiortb-

Syene his eji uickiiorm relicptis aquidiflantib.

Ov cu </ltxsx(r&s cu faf $ cu,tAiccySbjva-t [/>T&S$&^tplw a-cpcufoy ^tou^oiw^ 3Ttoff.7tf) %<££

t/liaJLgsySdiv f oc£&'* Kctfxyfoc

.*&\ ff ff» <- ufr^ fafc - fagtvv< fj uo ·% eccf^1£>07 f|

5

j4& 9 hk r owT&gttft

; |/u / 9» // s-. \$\£*Qey

5

j^ (/lixscca-fe-*ot/,' 5£*$ cck "-\^^\^\

cthriut^"<> 9 kft

Xfxmmy £ < o^tdsxo-ty^y^i $£

4t

Dfi INTERVALLO AEQVID I STANTI VM.

SEd ncc interualla drculoruin toto orbe a ie

iiurice ftata fun t : ueru pro fpha?raru defcris

ptione, adhuncmodu diipenfari folet. Diuifoin fexaginta partes meridiano quouis circulo,ie

ptcntrionalis circulus a polo iexagefimaru par^

rium fexjinteruallo defcribitur.Idem in alteram

pattem a folftitiali circulo fexagefimarupartiu

quinqpinteruallo notat.^Equatorab utroq? tropicoru fexagefimis quaternisdiftat. Brumaliscirculus ab antanflico fexageiimis quinq?. An*tardicus a polo fexagefimis fex. Neq?tamcn in

omiiiplagaurbeueeandcintercapedineinteric

feruantrfcd tropici ab axjuatoreparem in omnimdinauonediftaiitia uendicat. Iidemautab ar

&ids no pareperomneshorizotas, fedalibi minorem, alibi maiore . Itademu S>C anfhti a polisno parein quauis indinatione diftantia feruar,

fed alibi maiore,alibi minorehabet Sph^rse tas

menomnes ad Graccia^horizontadcfcriburur»S C L I A,

Proclusfdcitpartionmaauidifiantmmjuundumclm^

dumPartcs cmm yi. qualiumeflfphara Ix. fupermaxima ckcunfcrentU

conftituum gradut xxxvi.auahum ejl chcunferentidgrdduum cecb. Eiut

difpofitwcfi fignut mouetur ab V uerticecontra hori:;onthperpun

fta xxxvi. idemmalterampdrtem.) Secundumfexagefimipdrtitionent

fph*r*j4(itf<ddrdnfmtcr*<iHdtQr€m& b^olumpdna xy. Atdijlan

mwm

S / 4?tidktertqudtorm&tropkumtUtarcus G partes. &<ptdnthdsfu*perarcumertdianiB S partesyi. siergodrflicusdeftgneturaf st dcceadit ddtropicumin G ddpdrtes v.Hacdbmfpefiione fpharamukomdnifcfiiord hdbhur. M<p tdtnen.) Kdbtdt ergo drftuus exemplicaufafub dlio

fttufphtradrcum st minmmpdrteundqudliumfuithdflemspdrtiumirl Difldntid db eodd tropicum, ejlpartmm vl Rurjits dliofttu habcat smioremparteundtut v^. Difldntiddb eo ad troptcum,repericturpdrtmm«9. SicinreliqwquocutKpfitu fpharareperiturdlidVdlid difidntid,una

ffXdgefimdfdcitgrddusvi qualium eji circunferentia ccclx.

yOw^tiot€&% xzro Wwy vrtytQigiSiy

•rt)- nrotevs fe^ei/. &otou$Oi ,<& [9 rt9<*%. yoty 9$79· &%>

xAojf/ fei , ££ 730 \&«&7€(4/!/*. J

j> ot c/j&

T&y J>omK&y& ,- «ff » tQt (fiieugovcrt rcy jfe&%<rtoyT$iylot<AitoyKVKhtoy>

COLVRIS.

SVnt&C perpolos du&i circuli, quos nonuUlicoluros uocant, Iisaccidit,utinanibitus

fuosmundi polos recipiantColuriautem didifiint ,qubd partes aliquas inieminimeconipes

ftashabent Reliqui enim circuli in mundi cir^

cumadu integricernuntur.Sedcolurorum par

tes quaepiam, quseuiddicetabar&ico iub hori*

zontelatent,cerninon poflunt Signanturaus

tem hi circuli pertropicapuncfo , diuidutq? per

duas acquas partes circulu,quipermediafignis

feriducitim

f * Scholia,

*4'

S C L I ,Signantur.) Alteramborum F, udditperfigndtrophd GH. kl

ter C D perceqmnottiorumfigna c D. Relidut cirfw/i flwfxiflrnui

funtdefignati, emergentes conuerficne cceli cernumurper pdrtcr.fed colua

rorum pdrtes quapid, inquh Proclus,qUi£ ad dntdrttlciifunt,cerfii r.on pof»

funt. Atquialiciuofitumundicermetlihi integripoffunt . Keuoceturenim

fphara infitum fuUqumoftidlem, ut eum alids defignauimui.Vterdj colus

rvs bis confpic\tur,cumincidut diurnaconuerfione infuperfickm hori^oti:

itsjemelmatutino tempore, rurfus uefpmmo.Qiudre PtoUmaus eos cdfti

gdtius uocdt: hunc eumem per polos ofignd tropkd: illum euntem per pos

loso-figndaquinottiorum. SedProclus confiderdtionemhdbuitfpharxno

vn umuerfum, fed eius* dd climdgracumquod dixkfuper'ms)defcrtpta

foret. Diuidunt.) Smguliquidemdiuidutfigmferum CCDHifl pdu

tes bindsjed dmbofimul eundem diuidunt m pdrtes qudtuor,$ in Craca

leftione pro legendum.

7§««{/<$/\77<°&&yi7?¥*. j -¥ xocA«7?,*&ff

tcptXTifiTou </lvo ' ty^^ /v\

$9 vfi iiw&& ^'^^^7 $\ 72$) cuyoKiftoVS7>>7*> <f£ TJAecSf^^ 3& Asfc? kckKhtxu ZqhAmkos

D SIGNIFERO.

OBliquus circulus is eft, g duodecim figna

continet, ex tribus ^quidiftantib- circulis

conftastquoru duo latitudine figniferi determi

nantjUnus pcrmedia figna ductus uocatun hic

adeo duos parcs & equidiftantes circulos attin

gi t, fblftitialcm in prima cacri parte , brumale iii

capricorniprmdpio.Latitudo figniferi codnet

partcs xrj. Di&us cilauthiccirculusobliquus,

qp equidiftates ad in^quales angulos in teriecet.

» 4t

dfifav dltoylpy ,* ro

--^</ iiw ^·,-^^- /\\ yny€&~- \ yriy. ejcri <Avo> & cuobti*, KoyiM^^&$§<& Qftfey

\2Gro ?1 o4*®S7€^%/0 $\? cfxcnoos&s & { sxt/lmy

#£<%.^ hoyto ditofn&s ctft^y^y^ ^^&&pu>y hfxritos <^^^,^-* £ $\- tfiybgay (£? <fciy^\7<&&/&- <^<Poy u&i $~h cw-Tcg (PlxyJb/i , «sfc tcc^^^ KgU

?$ toc5/> <&*7{<f£sx</Uu>y ytt/oyJUcoy ffl tIuj ^x?i\ocylw ?1 »((>

yivtTva r> <^> i&i tfvcvwz

tcc&&'[&* c^e ySLvrot y\ rlw •vfyxTh.xylw5< rlw \zs\%-iiss sxflivs^<£& $\

tLjj7&£-7<*7 fi\ yXf u$i' 'T

<£)§«9/ oiKOvcty cbj? sx<Attoy^..$ <&0§©-5 q xutc^kj 7/ rn§a7tAk<rix cu i&m rot &^ cu& £< icrovim / «?<&··§7& oU

-u Clxtoc;

j >§7$ ^^, £>^ yiviofi& -^^^kj >&>^ iyu/ rce <^ !

j^ <rcpoufcus< curlcw%*^ ot /\ $>! *?

K?er \ </< ,' i&c xbv>i

Ttf,--^ ^ <&&^^ ccwt^

vxfiy^ djg,* Ǥ^ ogi-

, sgc<poyS(xtoy cdrrzoy <rcw[§cuvy/ ccy

vx%y kj xThorptoy · Ao^vasro y$b/7°tyc <?\

fiKng Qhkhs -r h%X$vr>2&o-ts kxtxvo^tou^

f DB HORU

4« F

D HORIZONTE.HOrizon uero circulus eft,quiconlpe&am

mundipatteab inconipeda dirimitJtaqjin duas partes uniuerfam fphscram fecat, ut alte

rumhemifphaerium fupra terram , alterumfub

terrardinquat. Eftuero horizonduplex, alter

quifenfu ufurpat, alterqui folarationeperdpis

tur.Ergo fenfibilishorizon eft, qui a noftro ui

fu in termino uifionis circufcribitHicadeo noamplius duum milium ftadiorum dimetietem

habet , Qui autem ratione percipitur, ad fixaru

ftellarumfphserampertinet,mundumcp totum

induo iecat Nec uero peromnem traftumurs

bemiieide horizon eft, fed feniii idem quadrin

genris fere ftadrjsmanetQuo fit,utdierum lon

gitudo Si clima, 8iapparenti^omnes esede fibi

conftent .Audo uero ftadiorum numero , pro

habitationis diuerfitatejhorizon^lima, omnesdem^apparmtiaemutantur. Couenit tamen,

ut habitationis ultra quadringentaftadia mustarionem adauftruboreamue accipiamus. Suquidemqui eundem acquidiftantem incolunt;

in quamlibetmagnoftadiorum numero, hori

zontaquidediuerfum habet: climauero idem,

&fapparentias omes fimiles. Dierumtamen exi

tiis initiaqp,haudquaqua i)s quieundem aequis

diftantem habitant ,eodem temporis momenj:

to euenient . Verum fi exaflae rationisexamini

ftareudimus,pro quolibetpu&o,in quauis or*

bis

hV

£ · 4f

bis parte mutati fitus, horizon,clima}& appa*

rentiseomnes euariant . Horizon uero earatio*nein fphaeraru defcriptionemnonadhibetuiv

quod reliqui circuli omnes ab ortu ad occafumrircuaclo mundouna rapiutur,horizon faa*

ptenaturaquietemarnat, eodemfemper feruas

to fitu.Si itacp horizon in ijphseras adderetjdr*

cumadisijs, eaam moueri,&:nonnuquam iu*

pra uerricem cfle acdderetad quodcote tumcaptum omnemfuperat^uma iphaerce ratios

neabhorret.Verumno incommodedusabaleueo,in quo iphserareuoluitur, intelligi folet.

. . . . IC L 1 A,

kon>n.) Ih conctpto organo efiafmilla fignh notata MKSC, ni*rfffeo.) Ouomiliaftadwrumreddunt cclx. M.paJJuuminterrd^iusnume»r\ medtetas ejlmiliapajjuum cxxv.per quantumfpatium amjiatm plantcie

terra marhue,prorfus uidet terram mareue contingere calum. Dr hoc horiZpntefenfibtli dixit Strabo his uerbts:Confequent(r ita<p huicpoethum illud

aecommoddtes,hori%ontem quidem debsmus acciftre, auodttrra uicinumfjioceano. Arfticumautem auod urret attiguum, quafi fignum habiuupdrtistmavmeardicum fccundum fenfum.cumprioreius traflatio futfjet

dchorizonte,quifolapercipuurratione. Quiautcm.) Oiximutalioca*pite qubddrculi circunfcribunt calefiem fpharamfola tmagmatwnc . Adhuncmodum hori^onmundanus calummedmm arcuncmgu, autemuhculo mauriali. Nrc uero. ) Tra{hm uocat chm<kclima uero( dif*

fcres fuus regionum, qualem habet una ukiniorem remotioremuc attera abtquatoreuerfus alterutrum mundipolum . Stadia uero cccc. reddunt xlvitj.

M. paffuui perquamufpatiumubi locusborcalior diflat abaufiraliori,fme

isabillofphararecipitalmfuiit cuiusfntxemplu:Kom

pra S horiKomlspundisxlii.QuiergolocummutetdifiamemKoma uerfusboredtn fiddijs cccc. leuabh polum amplim unofere punfio.Sed qui locummuut tatofpatio aufiralioreRoma, idedeponetfpharam poto piiilo uno \

fere minus parttbusxlij.proptcrca ut ccelitus apparentmrerum effe0ittstu*o!

rfpQndtmptrwintmiiatdjccsto 4dmtuuZc<tnonem* Gfacnitosta

4| 6 .dijsemm O.fecundurationemPioUmaiJiue D CC.fecundumueterufupt

futationcm conueniat mutarefitumfphcerapergrddum unum. Siquide.')

loca cjuxfnum habent diffcrentem interfeptentrionem meridicm:utfere

Cartbago<^Romathachabenthori^ontemuariatumfecundumfigna S.

Spbara cmm wj fignojit hoc loco aukm altero altwr. Roma quidtm partU

bus x/t;. Carthagmixxxij.Locaautemquafitumhabentaqualiterdtflantem

ttb aquatore uerum dijferentem,quid alter altero ejl oriemabor-.ut Conftan*

tmopolisipfacp Koma,b(£chcibenthori^ontemmutatumfeciidumfigna R C,

uideheetefioRomdfttdfub V uert'tce,eiushori^onejlper figna MRSC.Porrb cbfiantinopolis eji orientaltor Roma partibusaquatorisfere wc. Totu

demitacppambusquartte V R, reuocatafuper R fignumhortzontis,tfluer

tex Conjlantinopolis orientdltor V uertice Romdno.Et qutd per conftruttios

nem orgdm horizon©fuus ipfitti uertex dijldnt toto quddrdteugitur ho»

nzon Cofiantinopolis, dfldbttdfuo ucmce pcr quddratem, numeretur qua:

drdns ex loco uemch,Conftdnt'mopolis defigndto fuper qudrtd V R, dfidbit

horizonConfldntinopolis ex R& Cutrinqjtqudntumipfiuertices^nietur^

apud Rfubhorizonte.Apud C dutem fuprdhorizomem.perhos fines o-M

C S fignd tintelligdtur duci perpetuus circulus.li ertt horizpn:polisreprafentdtusmanentibusRomce.fubhoc fitu fphteraeuentuntutrotf

loco ftmditer dppdremia caleftes,quaUi nunc plurimd: de aqutdiftdntibus

C7- colur\t,v dierum prolixkdte dmmus.Sed hoc diffnunt, quid Confldntu

nopoli inuid dierum praueniunt Romdtid, cr tllic uefptr prauenit hunc ROs

tndnum fecundumrdtioncmdifidntia horfcontis butusdbillo quaeflhora

uniui (equtnottidlis& tertia pdrtis. Q«od tdle efi ubi Rcma numerdthordtn

undtn & pdrtem tertidmtdb ortu Confidniinopohsnumtrat hords duds cum

tertid pdrte db ortu: c? Roma qudtido meridies, Confldntinopolt eflhord fus

prd meridiem pnmd cum terttd unius : Roma qudndo occdfus Confidntia

nopoli hord und cum tertid nottis . Sed eflo obferudtio Confldntinopoh,fuc»

rittunccommutawlocofuuseiusfub V uertice,&horiz,onM. R SC.Exdlo

loco concipimus hdbttudinem hori^ontis Romani hoc modo. Differenttd lon

gitudmts utriufp efl noftrd, grddus xx qutbus eft Romd occidetaltor.ergofu

perqudrtd V C,totidem grddus djjumuntur ex V,dlic fitmintelligiitir uera

tex Romdnus. Ab hoc loco dccipidtur utrincp qudrtd circuli,finiet und db hos

ri%mteapud C, dlterd totidtrmgradibusfuprdhori^ontemdpud R.pereoi

fines& pundd S intelltgatur ducicirculus .Ii ejlhortzpnRomdms coU

lationecius ConftantinopoUi.Suntty hic rurfusfub duobus locis unius latitu

dinh omnid calnus dppdrentidfimdid,prater prceuentiones & confequutio;

na ortus& occdfus fic, utexemplopriort expofuimus.UdPiOclustdcitono

mine longuudinum, tdrum trdfldt rdtionem ,qudm nos prolixius enarrduU

mui, ut nunc edrum cogmtio pardretur, & pofiedin geogrdphicis longe fic*

rcnt mamfefliord^Uie tdnto antc meditatdfuiflent. Veru /i.) Dixit Pro<

S .clu:medmMdrtfttumfph*r*mdiftdnt'^adior^

rem rationem adducit, qua pcteflfic colligi. Gradus unus mcridiani, dmidimtelltgiturm rmmittas primds Ix. Porro Lc M.pdffmm terra.refpodem gradut unt calcjil Secundumhanc dflumptionem , efiobtm borealiorprimornille paffb.Uudbimusfphardmjubhoclwom potominuto uno dmpltusmerididMdfitu priorl Eflo rurfus locusfccudusorientaUorprimo millepdf*bbusfldtuemus uerticem loci orientaliorh proculunommtO,db V uertkebci primiuerfus Kfigmm, hocip feaudtur fuusillius horizonfecundumexpofitdm pdulb dnte rationem. Bodem exemplo mdiorib. mttrualla dfjumsptis, dptdbimusfphardmhancdd ccsleftis hdbttudinem.

rSoyfitto-Hyfytvvy LvtCKtoy*

tm^^l KOfvqlw&yfctcpo^®' » \<$ ffia&/ iic& , & -srom

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flvo-ty K01/loyyt/lctepofcuio"Hp£fivS^

DE R I D I I S CIRCVLIS,

MEridianusdrculuscft3quipermtindipolos 8ipunftum,quodnobis fupraucxtu

cem emine^&uciturJn quecumibl indditjmc^dios dies^ediasq^no&es efficit. Hicetia cirois:

tus,immotusinmimdo eft, uno eodemq^in to*

tamundiuertigineimiatopofitu, Nec in fphcc

ris,quiaftris infigniuturafcribitu^quod &:im

. g motus

f#

motus fit ,& nullam mutationem reripiat. Sed

(quod fenfu ufurpari poflit) treceris fere ftadrjs

idem meridianus manet . Rarionis tamen fcru*

pulofioreindaginead quemuis grefiun^qui or

mmuerfusoccafumue dirigit, nouus meridia*

nus notatur. Ad auftruenim boreamue quan«

tumui s progrediare5etiam fi dccem millium fta

dioruminterualluinterfit, idem meridianusfer

uatur, cum ab ortu adoccafum tur3niutatur.

S C L I A.

Semckcuhtsmcridianiefinotatusfignis V S, necinfpharhdfcribi

tur mier reliquos circulos, cequatcrem, pdrallclos, ecliptkdtn, colurosjed

exmnfecusadtjchurmfiarhortzotis. Seddubd.)Exfuperiorihypothefi

fladia ccc.dant xxxvi. M.pdffuil,dUdlwmflddidOJamgrddumum:fiut

ftadia ccc.dant xxvM.pdffuu }audlmm dcc. dantgradum circunferentiit

tnaximx, per quantufpatiu in terra, ubi difidt duo locd mteromntem&oc

ii<UntetmteBgiturmut0rimM

loci fcrupulofioris mdagnis,reycimus ddfitpmore cxplkationc de hor'u&t9

Ptei bi/Ktev*

lon ; <rui*san\ U/&&%&1<,0 tsty -&)*· iy&ysou. 3 «Sff, ijM& /*** ^tg»

tfAgsouq-&^ &^&,fcs-/ </£ / %'^.^^ ycty &T&yovq r>> Ktvfroy - . <# </£$^^('£<->& c c^gc ,ufc(rfc{/ ·?

jfaPmy. e/fgc ^, $ imslw bdfofrh%^^ -.LACTEO CIRCVLO.

ORliquuseriameft &laftcus drculus, Hic

kaq> fupratropicos obliquatus cernit.Co

ftat

.ftatautex tenui nebulofafubftan tia, unus certe

coeleftium circuloru conipicuus,nec certa latim

dinedefinitus, fedaliquafui partelatiore,aliqua

anguftiore. Quo minus equidemin plerafque

ipha^ras afcribi ibletEftautunus enumeromaximorumdrculoru; quippecummaximi drculi in iphaeris dicantur, quibusidem centrumcuiphseraeft. Suntporrbmaximi circuli feptem,

/EquatorjSigniferjquipermediafignaducitur,

qui perpolos dudtur, cuiufq? habitarionis hos .

rizon, Meridianus, Lafteus,

s c l . i

Vi4 ktfed per cjuas calipartes ducatur, traditur libro yli/ . magna compofttionis Ptokmcehquem locu ne<p totu defcr'tbimuitne(p relinquimus otnni

no. Delineabimus aut per eiusfumma uefhgta. Inhium ejlo apud Centauru,

unde peruenit uno margjneaddorfum lupi, altero adignem ara , hincpro»

cedk adfpondilespofirematfcorpionis margme boreali Jedaujlrali adpes

demprioremdextrumfctgittarij, mdeaquis laterib . peruenitad uulturem

uolantem,indeadgallmam : hmcmargofeptentrionalis tenditadcaput Cephei, undefpdrgitur in ramos, unomterorientemo-feptentrionem, altero

admeridiemo-orientem. Hac^onacomprehendit CafJlopeam,ldtus fepten

triondlegerw Kerculis: Meridiondle,ftelldmillius luciddtn . Hincldtusboa

redle tendit dd brdchm agitdtoris: Auflrale ad talumfimjirum ewfdtm.ttn:

de procedit ddpedesgeminom. Mdrgo uerb occidentdlis, comprehenditmanum Orionis, praterit duos cdnes , procedit ad nduim prope clypeum , inde

adinitiumredit. mmquiuoletdeftgndrejsperfuperftckmfphariedudflel

l* locatur,per auds ducitur mducet colorem candidiorem, rdiauQsfic ut in

coelo uia Idftea efi luce perfufior calo*T&yvTt»

·7·#\(/<{-^ ^ssi^ovQt^tAiM

g * 7r^s

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7$& » oU ^^&& 72J)«» xvigofioy^KfttvztKKhiivT?* kqofilovma

c/ oujTOti \2&7&- Kjfromxiioy*,.. 9 5i$><?eg*j&t?tof/ xi

ySLuy <. wr($& «/» Wgoc/Vi^\^ <*>

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DE Q.VINQ.VE S.

TOtius terrxfuperficies fpha?ricaeft,Srdiui

dkurinzonas quincj?. Ex quib. dusefunt,

qusecircapolos defcribimtur, frigidsedidse, q>

maxime abfunt a folis orbita : eaedem ob fngos

ris niuriam paruhabitatar*D etermi anturau*

te polos ueriusanftids circulis. Quaeuero poft

has deinceps habent5quodmediocriteradpra!<

tereuntem folem funt fit£5temperatae appellanf,

habentcp in coelo limites ar(fKcos5 tropicosq? cir

culos,quibus interiacet.Reliquajquasinterme«

moratasquamormedium locu tene^quod fub

ipfo fohs tranimnacer, torrida nuncupatur, a

terreftri ^quatorein duas partes diuiia: isporro

iub mundtaequatoreporrigitun Sedextempes

ratisaltera anoftriorbishominibus incolitur,

ipfalongapropecentummilibus ftadioram,la,

taferedimidio.

s c l .Totlus terra, calum non minusqukm terradimdimm qum({uci%ondi

tt&tWAi*. txhk duce funt , uidclicctqu& cx polis , " hts-uicms

2 » fj

figms L defcribuntur utrinque. \pfd longd.y Stcundum hypothefim,

qubd D, mi ferrd ddntgrddum unum mdxtmte circunferentue caU*

jlis,reddunt centum M.flddiorumgrddusducentosfuper aquatore . At Vto*

lcmaus extenditorbem habkatum inter occidentem c orientem grddibus

clxxx.fiue flddysinterrd xc.M.differentia eft inter utruncp finem grddtts

xx. fladta autem. M. Ldta autem. ) Oimtdium numeri prioris funi fids

dia mille quinqudgtntdjd efi,grddusfuper merididnocentu. AtPtolerhatts

finit orbem hdbitdtum uerfusfeptentYionemfub pdrdllehjiftdnte grddibus

Ixiij. uerfus dutem duflrum ultrd aqudtorempdrdllelo difidntegrddibuf dtn*

pliusxvifdcit tdHtudofuper drcutnerididnigrddus Ixxh.fiadia autein ter*

rd xxxixM . duingentd.PorroProctus de teperdtd uerfusfeptentrionem

folum uidetur:hac dutem ut IdtiJJtmd dccipidtur, comprehenditur inter pdt

rdllelosduos t huncperlAeroent illumper Tylen grddibus fuper merididno

xlvyfiddijs uerom terrd xxvij. M.quinghis.Ad hdnc rdtionem uelcorrigdn

tur numeri Proclidni uel excufentur:quonidm intdntis tendru fpdtijs, dein

de comtnentdrijs,o-tdbiilis terrenifitus differentibus dondndum duthoribus

eftji qutppidm cdlculo mdulferunt, ft<p fequuti diuerfdfueruni. Bttdmfic ut

ueteres omnes cofentidntttdmen noua hiflorid cognitijhdc <etdte quaqtidutf

fttm orbts cosomneiemendau

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y&f £<&/ «-ccs«g>&£7?. 'j §« &7& « 7i7oa<rrtr0g<iUi7f»

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D SIGNIS COELESTIBVS.

Slgna ftellis infignitadiuidunt in partes tres.

Quasdam in fignifero locataiimt, qusedamicptenmonaliauocanmr

5qu^daauftrina. Qu£itacpin figniferoiita funt, duodedm animalia

funt,quorumnomenclaturas alibi diximus. Inrjs duodedmftellasqugdamfunt^quseob qua£dam quas referunt notas

> proprias appellatios

nes meruerunt . Siqiridemiexnumero, qusc

tauri dorib uifunf,Pleiadas nominamnQuinsqueuero, quanncapite tauri cernuntur, Hya*des dicuntur. Stellauero,qua!pedesgemino5

rum praxedit, Propus quafi prsepes uocatimQuseuero in Cancro nubeculam referut,PncfepeuocantAtdua?quaduxtaPrsefepe collocatgiunt, Afdli dicuntur, Prsenitens autem fidus,

quodin cordeleonisnotaturjfimilicum loco

nomineleoniscordiciturranonnullisregiaftel

la,quod qui fub eanaicuntur, regiam natiuitas

tem fint nadi.Sed qusein uirginis fumma5fini^

ftramanu hxretjfulgidaiane ftella, ipicanomunantStellulauero quse iuxtauirginis dextramalafigitur, Prottygctes dicit Atquatuor fte%,

quadn fummaaquari} dextrauifunf,Vrnscnomen habet, Qux uero a pifciu caud^epartibus

f4

fite deinceps funt,graxelini}latine lineae: uel ut

quibufdam placet, lineolsenuncupantur. Sunt

itac^in auftrinalineafteltenouem.in feptetrio*

nali quinq$.Sedpr£fulges fydus, quod in fum*

malinea cofpicitur,gr2ece fy defmos,latineno*

dus nuncupamr.Septentrionalia {unt,qu£cun

que adfeptentrionefigniferi fitum habent. Sut

autemh#c;Vrfa maior, urfaminor, draco qui

interurfas locatArcflophylax, Corona,Eng05

nafinjSerpmtariuSjSerpenSjLyrajAuiSjSagit^

tajAquila^Dclphinus, Protomehippijhoceft,

prior equi porrio,iuxta ipparchu equus, Ce*

pheus5Cafiopeia5 Andromeda, Perfeus, Aurii

g^Ddtoton.Etquipofteaa Callimacho in a*

ftra rdatus eft,Berenices crinis. In rjs rurfus ftcl

l£qu£dam,ob notas quafdam integras,quas in

iecontinent proprias appellationes funt fortis

tae.Nam infigne fydus, quod fupra media Ar*

dophylads cruraiacet,Ar(5hirusappellat. Cla*

ra autem ftella> quae iuxta Lyram pofita eft , to*

rius figninomineLyradicit.Quxuero in Pcrs

feifumma finiftrafpedatur,Gorgone^nommhabent, Sedquaem fumma eius dextra notan*

tur, ftellubccerte crebrxparua?^, ialcemconfi*

dunt.Atilluftrefydus, quod in auriga? finiftro

humerocernimus, Capra nominamus . Duas

uero exiguas ftelias,quaein fumma eiufdem au

rigxmanu figuntur, Hocdos didmus. Auftri^

na fignafunt, quxcuq?ad meridionalem figni*

ten partem funtpofita,Eoru nominahscc (unttOrion, Procyon,Lepus

5 ArgcHydra, Crate*ra,Coruus, Centaurus,Feraquam Cetaurus te

nei^ThyrfoIochusqueCentauruspr^fertjThuribulum,Auftrinus pifcis,Cetus,Aquaqu^abaquariofunditur.FlumenquodabOrionedeifluit, Auftraliscorona, quam nonnulliurani*fcumuocauere, acfia coelo diminutiuum decli*

nesr&TiuxtaHipparchu caduceus, In s quoq*ftellaequacdampropriafibinomina uendicauererquippeluddaftellajquseinProcyonecerni^

tur,Procyonappellatur.Qua2uero in orecanisconipicuo iplendoreaipicitur,quod(^gftus in*crementafecuafferreputatur, caniseodemquototumfignu, nominecenfetur. At fidus quodinfummo Argus gubernaculo fiilget, Cano*pus nominatur. Hicin Rhodo segreconfpic^turvautcerteab^ditislocis, InAlexandriaueroprorfus non cernitur, utpote uix quarta figni

jportione,fuprahorizontemextante,

8 C O L I ,SMMi difiipfcwlwrw tiottihiiijlelldfuni & Proclo non commmoma,™*

Pleiadcs Grace, Latinc fuccul* dicunturjiue fidus parilicium, f«i Gr*ce

Protrygetes, latinc Prouindemia , uel AnteuindemiatortaltergeminorumappelUturTripus. DuxcUra mantmoribuscornibuscancri, vtresob,fcura uocanturnubilttm, luxtacaudam Uonis obfcurx vjt difiaBeremcescrincs. quampcdoreltoniscordichur, eademo-Tybtrone. Quamca»pkccdnis, Ifis uocatur: qu* uerbm orc, Syrius, aua& CdnicuU.Canopitgttiamuocatur, Ptolemcon. sigiaponbc<xlejlid,&corumfmgul* ftclU

rt

ficinfph<xrdminfcribumurt tabuUefl uocataraiicum fidUrum: vquam

nos aiio oprre in hunc ufum reduximus ex radicibus Ptolemai,dd xtatem no

firldnnii chriflinatt M. D.XXlIil.In illa m linea uocabult dffumptae,

fcnbicur mtmerusfub tnulo, fcenfio refta: itemaltus numerus e regwfab

utulodcdimtio. Afccnfio rctiatflaYculusmaxmus deftgnatus per polos

mundt S, o-quashtetf(^iionesaquatom,cuniigener'.sfiinrhi quosco

luroi uacat Proclur. mithimearum af.ennonum incioit infeft:one urrnd,

-fuccedhfupcr xdudtoremjtd uc numerusinlicat. Brgo dfcenfio rctld,cfi

d^lantidientriftellainfuperfKiecaiidmedietdtetotdcoluri ACB. De*

clindtio/ft diftuntid db xaudtore uerfus duflrii uelboredmfuper audc

libetafccnftone. Eddccipiturincirculis , quositocdt Proclus aquidifldntet

fub cdpue, cur aumq duntdxdt aditidifidntes, illtc m<ptiens: Qj(in &flelU

umuerfa m cequid-fldtitibus aradts quotidie fcruntur. Rurfusfiduvdemfies

ri neauit, ut ucl aflrd probe in fphcerd locentur fme ommbus aciuidfldnttbi

circuhs. Defigndnturdutem, utillic dtinotdtumefi , exutro<ppoh

B.&extctfioneperqudritbetfetimescoluri F.Eiusgenemfunt^

qwperfigna & H,cr G c? L dutitfumJetiiocomunisduoriuirculorH

(nempedfcenhonisreflcc&declindtioms) diciturradixcentri jiellaAgitut

ajfumatur fiella quxpidm, utpotefpkd uirginis. Afcenfio eius reftapraftrt

numerumgradus cxcuij. o-femist ajfumaturfuperfphcerdpiinflum<€<iud:

toristotidempdrtib.diftdnsexcoluro CK.Upunftusfidtuaturfubars

rmildm AE B. Oeclindtio porrb dlicm tdbuidfcribitur A,X,idefl,au

firdlisab neaudtoregradus x. Ergonumertnturex A£ fignouerfut rori

dempdrtes,incommumfett'tonefpk<ierce&dmilU AE B.ftgneturpuiu

flus fuper fphcera. Edefipofitio fpicae uirgmh refpondemcognatoloco mfuperficiecab. Loeaquoquein terrdtnfaibuntur eademrdtione qudflella.

Sedfupputdtlofupenequdtoreuddit contrdrio modo,c fidtmtur initmm

apud D feilionem,fupenptotofemkirctilo D E.qmperinfuUs forttts

ndtasduchur:indetycrefcuntmmeriuerfiisfcmickculum ,finus ingrddibus clxxx.indeq dd mtium red:t. Oeinde quaillicdfcenfionet

rctta, hic loguudinss: c? aux illic declmationes,h>c Uthudms cenfentur*

E/mj c/io excmplum urbs Koma . Longuudoex D grddus xxxvi . cum

dudbustertijsjdtitudo xlij.fere. Pxddiceset<am ftclldrttmprcetered figuna

tur fecundumpofitionem adeclipticdm^Utiradices prope fola obferuana

tur. \n tabuldflelldrum m Ivned uocdbulifiella, fcribhur mtmerusfub titu

io, longttudo: Uem dliusfub thulo, Latitudo. Eflf longttudocirculusmde

ximusdefignatusperpolos L tclpucce.o-huiusaMdslibctfelliones^cue

hsgcnerisfunt vi. defcrlpti m fphxra deftgndntes xij. iriuid fignorum^o

imci. Initiumlongjtudinuminciph afettioneucrnddpudct &fucceditnu

nurm

* tn

merusfccundumfignorum zodidci ordinem, Ariet, Tdttrut,* liqttd . Er*

golongitudofiellaefi ciut diflantiain fuperficietotdcceliextotdmedietds

te C L. Ldtitudo ftelUefieiuidifldntiddbeclipticd tterfusditftrumuel

borcdm. Sunt dutem hi quoque tquidijidtesfibi & ecliptiae defigndti ex po

lisK&L tdnqudtncentrh ,o-qudhbet fettionc circuli longhudinis cL. Eiusgcnerhfunt aquidtjldntes xy. ipfi cdiptkce, qui utrmque finluntUtitudtncmzodidcL Horum ctrculorum , nempe longitudinis o* latitudmh,

communisfeftio eflrddixfielU. IgiturfufpenddturfphardinpolisK cr L:

fmeiubi idefi mims commodum) polus L ecliptlcajidtuaturfubV fignum

uerttcis, tta ut tota ecliptica mceddt per totum fitum hort^omis ,cdnccr<p

apud VL.Cdpficorms apud s feftiones hori^ontho-meridiani ,Lit>rdr

<pds

pttd R,? Aries dpud C communes feflioneshorizomis o* aqtidtorh, o*

tcltpticafldtudntur. Sicconformdtd a-confirmatd fphcerd,infcr'ibdntur

auotlibetfiella.qudrum Uthudo eji boredlis. Efto exemplt caufd Arilurus,

tongitudoefiLibragrddusxviij .mmut'ueprimce v. Uac pars figni affumd;

turfuper fph(erd,tllucddmouedturqudrtd V R cum eiusldtereeunteper

centrum V ucrttcis.Lathudoponbillicintdbuldfcribimr xxxi.c fe=

ms/^fiboredlis, totidempdrtium. Ergommerentur fuprdqudrtd R V,

tx R totidcmpdrtes,o-incommunifefttonequartao-fph(er* figdturpun

Hum Miufire. Raccfirddixcentri Artiuri. Pro ftellit, quarum ejl Ut tudo

dujlrdhstcommutanduseJ}fitusfpbiertt,ficutpolus fifidtur fub V utr*

ticemjuerit tunc Cdpncornus dpud M.Cancerdpud S Jc0iiones,Librdds

pui ft tAriesdpudc utpr'idem,reliqud<putfuperius. Eiusefloexemplum

fpicdttirgmir.qudm rurfus dffurmmus, ut demuscldrum experimemum,

qucmadmodumutrdqrdiix edndepofttionemm fphcerdfdcitficlU. Longi

tudoeflubrx xvij. cumundqumtdpmis. Ldtkudo A,idcfi,duftrdlisduo,

bitvumerenturfuperqudrtd R Vex R. qudrtducrbddmouedturfuperpdr

tmlonghudmnfaLibra,tuncmcommumfe0ltonequdrta o-fphjtrafigd

tur pundum, rddix centri fpica wrgmit. Hic in Rhodio. ) Rhodus latia

tudinemhdbet grddus mgmtd&fex. RddixCdnop'it quce propiorfitatdti

Procli, Afccnftore&d ixx.femis. Oeclindtto xlix. femis: fccundum hdnc

rddicempondturfielldin fphcerdm^onformeturea fecundum fitum Ales

xmdr\ce,mtrfusuideliturpelus fub fignum hori^onth, quotpdrtis

bus polui leuatur fuprd S, nempe xxxu Defignetur igkurfecundum

hds partcs AntdrSiicus M,mdximus limaillic Alexdndritefiderumfemz

per occultorum: fedis efibreuiorpunttis nouendectm, eo aquldifldnte du*

perrddiccm Cdnopi. Ergo ftelld longecmmet fuprd hori^cntem Alc*

Xdndria grdd bus nouem , fldtudtur fpheerdddrdtionem climdtis nhodit

tnfit, Amdrttuus U comperhurireuio^aquidtfidnte dufloper Rko*

h dumgradk

f* » * .zhodum grddibut quvn^ue mtrUiant fcre. At is eft breuior pttnfth qttdtuo*

-femis, eo aquidfiantt dutto pcr radiccm canopt : ergo Uuaturjielk illic

nhodigradtb. quatuor vfemis. Ex hac oflenfionecOumclturerror locipr*fenth: non enim prorfus non eerni poterlt Alexandrice, qui Rhodi cernitur,

quin illic magis csrnetur,auanto maior ejijidla dtitudo. qparta autempars fignijuntgrddusfeptemo-femis. Hac kttio fuut altena

k potcftcu

tefphara, ftc ifiud fucrit alknijp.mum, ut lapfum tam mariifeflum trthm»mus autori

. Nos adiettum dicimus lekore quopkmparum cauto. Sifuide c? in reliquis partibus eius capttis, nMjiei

laritm attigit ampliusfupra nomcnclaturam,

Votuit crgotodem cxemplo hicetit

finire fermonemna. Atfydus

quodmfummo Argus

gubernaculoful

gct t canopus normnatur.

FIN13 JPHAERAE PJlOCLt.

PARI

PARS ALTERA DE CAnONICAPER SPHAERAM OPERATIONE,.

Adenus iequuti Proclujfecimus nudam indicamradrculorumiph^quibus coelitusapparetesrcstranfis:

guntur,Secundum id5aperiemus fe^

quetifermonecanonicamoperationem5motus

codeftisimitabilem nobishocexemplari orga*no . Totam autem operationem , adpauca atq?haxneceilariacapitaadducemus.Adhoc ueronegotium praxipuepoftulantur, quarin indu*dionediximus, ut machina ftatuaturin plani*

ciemcorredaquaquauerfumad^quilibrij exa*men, utcpmeridianus s ftetiuperficie mesridiani coekftisjfiuequod tantundem eft,in \&neacardinis fecudummagnetisregufam,Vtueroarcus s B,adcertumutillicnumeruaflumai:tur, interimno requirimus, fed alterum hoc, utgradusfolis certus fitaddiern

}fub quofit ope^ratio , Is autem ficprope aduerum concipitur,

fol ingrediturinidafignorum circiteridus menfium , utarietem circiter idus Marrias , taurumcirciteridusApriles^

Siccpfignareliqua drciterreliquasidus, hasra*

tionegradusjfinguli eclipticceab initfjs fequcrii:

tesjtribuutur fingulis diebusfequentibus idus,

& obuenietgradus folis,quo cum eritad diemoperandum.Quod fi idem exade queritur,tra*

ditus eft canon in opereSaphe£5 undepetatur,

h | CANON

CANONICA SPBXERA8.

C R I V S.

DB CIRCVLO ALT1TVDINISuerticalifolis,

Clrculus altitudinis defignaturcircino cx

polo horizotis utcetro>&: extenfionequa*

libetperquempiamuerticalium M,uel R,uel

V c, uel s : funtq? in circuli ex genere sequidis

ftanrium horizontinumero xc inftar aequidi*

ftanrium axjuatori ,per eos captatur eleuatio fis

derum fupra horizontem, Vcrticales funt=tionescirculorumin fphxramaximorum, ue?

nicntes ex uertice&eodem polo horizontis, fu

pcreius quaslibet partes,funtcp in fuo generead

horizontcm quodafcenfiones redaeadsequa*

torem,& longitudines adeclipricam, pereos ca

ptaturdiftatia fiderisexmeridiano , fiue

«,quartacv r&vc tenentuice,&:faduntoffi

dum. Pro uerticali condpiedo, index ftatua*

turfuperquartam uerricalem,refpidetemad re*

gionem fideris inparteccdi. QuartaauteniOis

ueaturcontra fidus,ita utumbraex apiceindi*

cis ingrediaturpermediam fpinam quartae. Arcus horizotis interquartam &latus meridiani

uicinius notatnumerum uerticalis, ideft, quan

titate diftantiae fideris a meridiano . Efto exem*

pli caufa quarta R per qua fitoperatio, arcus

R s notatdiftanriam ex imo codi>arcus R Mdi*

ftantia ex medio cocli.Pro altitudine contipicn

da5manetequarta in fitu pr^fmri,moueatur in*

R I . «I

dex propius lSgiusue ab alterutro pu&o V, uel

R ad alkjua parte,ubi ndex confiftens,eiusumbra in pede cotrahatur 8i tota abfumatur. Tucpes indicis inter diuifiones quartaefuperiupre*

maipina3indicataIdtudineexhorizote, Arcus

uero quarta? apedead fignu,indicat diftantia

fideris a uertice. Latera quinetia indicis deiceru

dentia per iuperficiem quartse, indicant inter di

menfioneslaterum eafdem, cum altitudinemlu

prahorizontem,tum diftantiam a uerrice/

C I I.

DB LATITVDINE LOCI CONClMENDAex althudinefideris© uerthali dattt*

LEuabiturfignu B ipha?ra?ex s horizontis,

hacflenus quodgradus iblis in eclipticano^

tatus,addiem admotus fub uerricale,incidatpa

riter in depreheniamalatudine.Hocfitu arcus

V eft quefitalaritudo loci, id eft} diftantia eius

uerilis boream ex perpediculo a?quatoris, Sc ar

cus s altitudopoli, parubiq? laritudini con*

ceptae, Ergo alterutro arcu explorato3 alter eft

exploratus.

c .D GRADV SOLIS C C I D Dad diem ex altitudineo uerticali, ex que loci latuudinedatis.

GRadum folis pridemconcepimus ex ratio

ne extrinfecus peritajUeru hic eudem con*

dpimus ex ipfapoteftateiph^ra?.Altitudine Si

uerricaliconcepdsj&arcus afTumptofecuns:

dum

« CANONICA 8 SFfiAf RAW.

dumlod btitudinenijmoueaturiphscraabor*

tuin occafum, donec gradus quiipia eclipncse

ueniat fub datamfedionemaltitudinis 8i uerti

calis, quiinciderit,efl:illic quefitusgradus folis

ad diem. In eodemgradu uoluatur ipharra fubmeridianu ae B.Arcusmericbanimtercon*ceptumgradum 8cae fignum medius,eft decli

natio prcefens folis ab sequatore, Deniq? arcus

meridianiinter Mfignumhorizontis &gradupracfentem, eftalatudoiblis meridianafub di*

em conceptum,

C I I l U

L I CARPINIS S, C 5 btuenda m planicietexaltitud'mefolts mcridiand.

TRanfponaturindexfuperarmiUam m vinalritudine meridianam exploratam,&:tem

poreuicino medi) didcontinueobferuetur>&

dirigatur inftrumentu hadtenus quodtempusueniat, quo umbra aflumatur in pede indids,

nufquam dedinans amedia ipina.Hoc fitu^ganipedes dus qui defcendunt in planiciem ex

8 s fignisjftantinlineacardinis, fiuefuperfi

demeridiani mudani,notetur is fitus RgnisySC

per hsccducatur hneaperplanidem, adperpestuuufum Pedesquoqjorganiquidefcenduntinplanide, exR &C c fignishorizoris, ftant eos

demoperainlineadecumana, quataealongifli

meinterortum 8c occafum exteditur, fignetur

R ' f 0. €f

ipfaquo^Gradus quo^£quatoris,qui iimulcumgradu folis ftatfub meridiano,uocat afcenfio reda,gradus pr^fentis deecliptica

5&:infigni

ternateturmancpeiusufuseritadfequentesplu

rimas obferuationes.Denicplineacardinis s9

poteftconftitui quolibetalio extrameridie tempore. Eftoexemplicaufatempus iftudmatutunum, gradusa^quatoris : illa dico afcenfioredagradusecliptica^ dimoueaturexmeridiano uerfus R horizontis, pergradussequatoris quotlibueritTuncperlocumfolisineclipticaeduca.:

turquarta R,&noteturalritudo folis ex hori*zontein hoc fitu, illuc ftatuaturindex, Poftdurigaturquarta R continue

5motu totius inftrumenticotrafokm, donecoccaiioinddat,utumbraabfumaturadpedem indicis, fuacp ipfiushGtudocomplecfiaturutroqpfinelaatudinequar

ta^neutro latereex ea declinans . Vbi hoc deprehenfum fuerit , armiiia v s, quareipidt,indeinceditfuperfides meridianimundani ,& linea

s ftat in linea cardinis,noteturea perfummospedes organi, utdictum efi

c .DB ARCV DIVRNO N0CTVRNO

ajfumptogradufoUs.

COnccptMsgradus folis, ad diem ftatuatur

in alterutram fafiionem horizontis, orien

talemfiueocddentalem, Eftoueroexemplicau

i fain

<5d. CANONICA SPHAfiRAB

fa in onentalem ,fuperautemaequatorefiatnoi;

tafub AE fignoc5muniipfi &meridiano. Abhoc figno xquatoris numereturfuperipfo gra*

dus ufque ad afcenfianem re&am pridemcom

pertam, is cft arcus femidiurnus , is geminetur,

& prouenit integer arcus diurnaereuolurionis

folis fub aiTumpto gradu. Is arcus diftribuatur

per v. proueniun t horae 8C partes prolixitas

tis dieipradfentis, Itemarcus diurnusfubtrahatf

tur degradib. ccdx, fiuenumerus horarum di*

urnarumfubtrahaturabhorisxxiifj.refiduum

eftquantitas no&urna, Quotgraduumiiiper

sequatore eftarcus,uel s no&urnus,uel illediur

nus, totidem etiam cft idem arcus fuper paralle^

lo folis pr^fenri.Igiturarcus ^quatoris diunius,

numeratporrionem paralleli diurna,& nodhir

nus diurna. Haeccp eft uniuerfalis rario,qua cos

gnofcituromnis paralleliportio fuprahorizon

temleuata , &C porrio reliqua fub eode depreila.

Etqua plane enarratur, &ponitur in exemplu

caputProclijde occultationib.&cmerfu fideru.

C VI.

HORA D1VRNA D V S.

HOra eftinteraallum temporis conceptum

fecudum aliquot partes, uel gquatoris uel

unius illi sequidiftantiu.Ea interaallaailumun

tur,uelperaequales «trcusfecunduomncsparaU

lclos

8 R I ,lelos, utpunctaquindena, 8ihx dicuntur ho*raeaequales, fiueperpunda insequalianuncpluraxv» ut in fignis borealib, nunc pauciora xv;utin fignis auftralib,& hae dicunturin^quales,fiuetemporales^affumuturfecundum hancratione,utomnesparalldi feoriini portionenidiurnam parriamurin partes xquas. &feorfimnocflurnaminxrj* pofteahoraea?qualesua

rie numeratur. Aliquseincipiuntex medio die,

8i definutadimum coeliad xrj. Hincruriiis abunoincipiurtt, &deiinuntad medmmcceliinx^hacferedkunturasquinocfliales. Aliseaboccafu folis ordiuntur, d>Ccontinuo incremeto fiic

cedentes , finiutfub occafii folis diei iequetis in

numefo xxiirj* Siue ordiunturab ortu, ScRnuuntfub occafum eius diei in numero quantitas

tis diurna?. Rurfus fub occafu ordientes}finiut

fubiequentis diei ortu,innumero quantitatis

noAurnae,Hae horscequales tantum dicuntur,

non asquinocfliales.Hora sequinoftiaHs fic concipitur : Concipiaturaltitudo & uerticalis folis

ad tempusobferuationis, fub hunc locumad*moueatur gradus folis , tuncportio sequatorisdeprehenfaintermeridianum &Tnotam afcen*

fionis re&se, ipiius gradus notat horam, Eftohasc portio ab ortuad meridicm

, gradus quin*deni ex meridie notant horam xi, triceni dedsmam, quadrageniquini nonam. Adaimmoidum diftribuemus horas reliquas, occurretfug

i * nota

6« C ANONICAB SPRABRAB

nota afccnfionis re<fbe, gradus folis denominae

tio horac& partis. Veru efto obferuatio tempo

rea meridie, gradus a?quatoris xv. a meridie di

cunthoram prima, gradus xxx. horam fccuns

dam: atepadhucmodum diftribuentes arcum

icquatorisjcadetfupernotaafcenonisrecrt^gra

dus folis denominatio hora?pra?fentis.His hos

ristotaprope Germaniautitur. Hora ab ortu

folis fic exploratut\Gradus folis ftatuat in hori

zontcmorientalem, &not€turafcenfio redafo

lis.Ab ea gradus xv . danthoram prima ab of*

tu,gradus xxx. fecundam,gradus xlv, tertiam.

fic continua fucceffione per incrementa hora*

rum, ufq? fub occafum. Prarterea notetur arcus

scquatoris inter R fignum,& afceniionerh recfta

folis interceptus: Is arcus dicetur a nobis diffes

rentiaafcenfionalis, habeaturmemoria quot is

graduumfit, Hisita compofitis, ftatuatur ut

anteagradusfolis fub fedionem alrirudinis &uerticaiis, deprehenfam ad conftitutum tems

pus,tunc a loco aequatoris^qui diftatex R figno

fecundumnumerum differentia? afcenfionalis,

memoratscnumerentur hora?,ufquead prseien

tem imimafceniionis recffec, prouenitcp deno*

minatiohora:temporisexacfii abortu. Hisho*

ris duo Germanisepopuli utuntur, Norinbur

genfis,& Ratifpontanus . Hora ab occafu*lis numerata

,ficconcipitur . Statuatur gradus

infuperficiemhorizOntis occidcntalis, dCnote

tur

turafcen fio refta folis,ab eaindpiuntnumerari

horsepergradus quindecim 2equatoris5ordien

tesab una, itau tin hisab ortu diximus, Note*tur arcus aequatoris inter afcenfionemrecfhm

folis,& c fignum horizontis mterceptus. Is ar^

cus itautprior, diciturdifferentiaafcefionalis,

teneatur memoriter quot graduum fit, poftea

locato gradu folis in fedione altitudinis& uen:

ticalis,numerentur iiiper xquatorcexarcu pari

differentia? aicenfiotiali horx ordine cotinuo,

ufquead afcefionem gradus folis,iuper ea pros

uenitdenominatiohor^temporis exadi ab ocs

cafu,Hora diurnaina?qualis fic accipitur.Semi

diurnus arcus folis repertus, per canone quiru

tum diuiditurper vi.&proueniuntgradus de*

biti interuallo horseunius ,Tuncfada ad teiru

pus obieruationeper altitudine &uerricalem,

arcusa^quatoris interdifferentiam aicenfiona^

iemortiuam, &pra?fentemlocu afcenfionis res

itaedeprehenius, digeraturper fa&ainterualla,

&C prouenitdenominatio horseinscqualis Hisolim Romani}Syri,ferecJantiquitas uiafait, II

lis uero ab occaiii utuntur hodieltali, Boemi,

8iPoloni . Ha-c fic exequi perpartes oportuitt

propterea ut Proclus intelligaturapudomnes

communiter, qualicuncgtandemillipartidone

temporis &adnumerationeutantur,

i 3 CANON

CANONICA SPHAfiRAB.

C VII,D ALTITVDINE S0LIS SVPRA

rbiontcm concipknda ex dato locofolis in horu.

AScenfio refta, gradus folis ftatuat fub mes

ridianum M,inde dimoueatur uerfus R

fignum horizontis, iecundu partes reiponden

tes interuallo horaeunius sequino&ialis, fiueiU

Iiustemporalis;harumnanquemeridianus efi:

seque mediusjfecundudenominarione 8cinu

tiu horae integra?.Hoc fitufph^ firmato,quar

ta Radducat fupergradu folis, arcus quartsc

inter R fignudus,fiuefuperfidemhorizotis&

gradum folis,deprehefus eft altitudo fideris ad

horaunam dtro ultrouemeridiem quefita. Eo*

dem exemplo in reliquis fiatln horis ab occaiii

Si ortu numeratis, Gradus folis ftatuatur in fu*

perfidem horizontis orientalis, &C obferuetur

gradus aequatoris exiftens in medio coeli,is gra*

dus dimoueaturexmeridianouerfus c fecun*

dumpartes v.Sub hoc fitu trasferaturpergra*

dumfolis quarta R,et arcus huius interfuper*

fidem horizontis& gradum folis deprehen*

fus,eft quefitaaltitudo. Cuuero ad tempus fue

rituentummeridianum, gradus folis fteterit

in medio cocli,gradus a?quatoris qui eft afceru

fiore&a}ftabitin c fignohorizontis.Ergopro

horis reliquis ameridie,dimoueatureadeafcen

fio re&a ex c, ueriiis imum coeli iecundum gra

dus xv# pergradum uero folis exteiidaturquar

tavc

R I .ta c, &arcushuius mterhorizontem Sclos

cum iblis eftaltitudo.Ver5 in hishoris ab occafu numeratis, euenietquod ortus iblisnon inci

detin articulos hor£integr£}ergo quodrdiqiiu

eft, ad iequentis inirium capteturiiipersequatQ

re, tantundemcp accipiaturex afcenfione redauerfus R horizonris,Etpars sequinodialis qu£attingimr, efteadeftinataad operatione, fecun

duminiaa horarum numeratarum aboccafa,

C VIII,

DB VMBRA EX ALTITVDINBad horam conflituendam.

DVcatur extrinfecus in abacoper mediamplaniciem tanquam horizontem linea

B,exquaaiIumaturporrio c,eftc fignumlo*cus Sdotheri eredi in planide. Ex c educatur

perpendicuiaris c D,uidelicet axis horizontis,

exeoaflumaturporrioc proceritas Sdothe*ris,ex quaducaturperpendicularisad C D,£quidiftansautipfi c qucefitE F

5&Tcentroeducat

quadranscotingensfigna F D, Is in fphara, re

prafentat quartam qualibct defcendente ex

uerdcefuperplanide,&: C refertquamlibet

medenteexaiTumptislliperhorizoteiigniSjdu

&a permediucentru. Quarta diuidat in pahesaequasxc. infcriptiofitexFin d. porrbSciothe

reus c diuidafin quotlibetparccs £quas,Efto

uero

CANONICA SPftABRXew

uero exempli caufa . iecudum ratio*

ncm aiTumpta, quod pedes vi.&Tfemis,

reddantfuam cuiufcpmenfura 5&SciOi

thereus referat ftaturam hominis obfer^

uanris.Sciothereus c transferatur cu

cirdni aequilatationepertotaplanideni

, 8chaxinterualla fubdiuidaturper

trededmaspartes c EjinfcripriofitexC

uerfus B:atqpha?ceftnoftra?defcriptiOii

nis formula. Nunctandemueniamusad umbram colligendamex altitudine

quacimquedata. AfTumatur alritudo

adhoram datam.Efto ha?c exempli cau

iameridiana,capitis arierisgraduum xUvirj»in latitudinelodgraduu. ha?c

altitudo numeretur in quadrante ex F

in D,Hincftatuaturregula,&tranfiriit

taturper medium umbilicum, note*

turcpfedtio in , fithaec c EftumbraG meridianacoceptaex dataaltitudi*

ne. fic in reliquis operandu eiiPofthecT 1' I 1 w

>

6 R I . 7;

digerantur tabe%certis areolis:aquamm fron

tefignentur partes zodiad,exIatereautem de*

fcendentefignentur horae:& in horum comu*ni angulo notent conceptse altitudines

5&um*brasfecundumformulamfubie&am.Qui uero

iftaparaturus eft,utex his obferuetjdebebit afc

fumeregradus denos fignorum, quoru anno*tabit altitudines&umbras perhoras fingulas,

quo exadius obieruatio refpondeat ad coelefti

um habitudine, nam ita utnos perfumma fig*

norumcapitatabulas digeffimus,non poteftal

titiido h^c, &Cumbra exade fatis pertotumreli

quu fignumindicare,Sed nos exemplu ^ppofu

imus,quodefletundeopus abiblutu deforma*ret, Quiuelitper memoratasumbras obierua*

re,conftituatlocum iblis in fignis,perea qug: ini

tio canomcasoperationis prsefati fumustetiam

conftituatgenus horg.Efto exempli cauia eius

ab occafu.Secundu ifta,obieruator ftet redus

in ueftigio:etnotetfinemumbr^ ex uerticeper*

uenientemad planitiem :etmetiatur aplantaue

fitgri pedes medios,quifuntadnotam finisumbr^cumhocnumero ingrediaturtabulamfub

figno concepto, Numerushorsee regione,eft

ca qucefita, Sed eueniet, quod idem numerus

non reperietur fub figno concepto.Hic ita erit

ad,ppinquam rarionem operandu. Eftoexem

pli cauiaobieruatio fub figno capricorni.Vm*bra deprehenia3

eft pedum mediorum xxxv,Isnu

? CANONICA SPBAERAB

Is numerus non reperitur fub limite,fed pro*

xime maioreo ,& minor .Ita*

que ut eft medium adi & > ita momen*

tum obferuationis , eft media hora ex i ad

xix»

C IX»

DE ALTITVDINE SVDBRIS, AD HO

ramt de$ linea cardinis& bttitudmc loci confiitucnda.

HAc uia ueteres ufi fuerunt dimatibus in*

dicandis,fub mcnrione habitudinis mu*

tux gnomonis ad umbram. Ergo hunc cano*

nemtra&amu^unde dusorigo habeatur. De*

indeiedori^uo ipfius iudidoftet cenfuraqua*

tenusprobetumbras, quacin operedere rufti*

caapud Palladium extantVmbra deprehenfa,

transferaturparinumero inpundaplanidd ex

c in B,PcrhancnotamctEccntrum,cijdatrcfia

iti quadrante F D,Arcus dus ex F ad lineam, eft

attitudo refpondens dat£ umbre.Efto exempli

caufaobferuario hxc temporematutino.Igitur

reliquum operis,agemus perquartam R fphg

noftrae.In ea ftatuaturindex fuperparem *U

titudtnem ex R, SC continue obferuet tempus,

& quarta R contra fydus admoueatur: quod

tandem indexdusabfumatumbram infemet,

denicp lateribus umbre,comprehendatarmilla

craffitudin^exea nufcp declinans. Hocopere

ftatarmillas VM }infuperfide mcridiani mun*

dani.Porroconrinenti operefignumB moueatur

ft . . 7f

turexs haflenusjquodgradusfolisconccptus

addiem fuccedens quartae R,attingatpundualrimdiniscomperoc. Hocfitu areus meridia*

ni AE,notat latitudinemlod.Nuncad nurne

rosumbraru Palladrj accedamus.Opus hic erit

utfcioteres c diuidat inpartes I acquas, eaqj

scquilatario transferat in planiciem c Jta uetc

res uii fuerunt,tanq? pedes reddan tfuam cu

iufquemenfuram.Ergoaflumaturex Palladio

umbra.Bftoh^cmeridianaadmenfem decem

brempedum I x.hdcc redditper fuperioreopc^

rationem altitudinem inquartaF D graduum

. Aflumat ei in fphaera noftra par ar

cus meridianiex uerfus v,fubhoc uero diefol

decurrit gradum fagittarij circiter i , Is gras

dus edipticaeC g d H,ftatuat fub meridianum

in notatamaltitudinem, &arcus ae meridia

nf,notatlatitudincmlocigraduum ,Adhunc modufioperemurperumbras reliquas,

debebitexomnibus fimilitcr prouenire arcus

AE v3parhuic latitudini. Sedexperienri in relu

quis,ea haudqua^prouenit3quin ut fecundu

quancuncp umbram aiiam5tanquamfuperio5

rem experimentum fiat,reliquae uiciffim adean

dem norma non refpondebunt:& licet depre*

henderequod promifcue arguant latitudines

locorum a Carthagineper Skiliam, perqjtatis:

am3ethuius ufq?regionemVcneriam,adquan

tam diuerfitatemunde potuerint aflumi uro*

* brac

7« C I C S R.br«r, tauquam uni dimati refpondes, neicio,

nifi indeforfan,quod umbr^authoriscumnon^qualiter refponderent lods diftantibus, emendauit in eo unufquifcp numeram

}qualem umbreprafenti pro loco conuenirefenriebat.

c x.

D FICVRA COELl, DEQVBemerfu & occuhationefyierum.

Flgura coelieftdtfpoiidoipiius, utscquator

&C zodiacus,utcp imagines et ftellsc finguta:

^pueft^ fint conuerfione cocli ilib confideratios

nehoras prccfentis.Ergo foleud no&e ftelia alis

quacollocatafub horam ex ucrticali &altitudi

ne,reliqua omnia, quse defignari in coelo po&funt, funtcoordinatafub parte cceli, ad quamperueneruntruidelicet alia ad ortum, aliaad oc

cafum,aliaq?admcdtum ccdi, autad alias pafi*

tiones parriculares. Siccaptatur ratio ortus&occafus fyderum, dequibus funttam multaa*

pudauthores.quorum gratia harc etiam adiun

gemus.Hcliacus ortus3fyderis eft emerfio exra

drjsiblisjfic utlongepraeueniat foiem matutis

no,ucl fubiequaturuefpertino.Heliacus occas

fus5eit{ucceffio fyderis fub folis radios,fic ut in

ccelo non compareat. Cofmicus ortus,eftqui

diumus:etiigiiumcofmiceorirididt5quodoc

cidere heliace prius diximus. quia enim in par

te coeli cum fole fertur, oriturpariter cum eo,

quo cum fertur:ut, Candidus auratis aperit

cum

R 1 , ,

cum cornibus annumTaurus.CoCnicus occafus, lyderis eft quo ipfum fimul cum fole occu

dit.Sed& coimicus occafus eft, quo iydus ocddit(utpoteapud c horizonris)foIeexdiuerfiiIi

ma partecoeli(utpoteapud R)oriente:ut,Antetibi eose Adanrides abfcondanf, Debitaquamfulds committas feminaterre.Satis enim fitau*

tumno cumfol eftin icorpione. Atlandidumautem radix conftituitur in tauro,diftante ex

diametro afcorpione,Non pofliint igitur ab*

fcondi aiiarattone,quamquoddefcendantfubhorizonterdefcmdunt autem tunc,cum ibl ex

aduerib orit.Acronydus ortus eft,qui nodturs

nus,quandofyduseiTiergitapudRhorizontis,

foleex aduerfo occidente:ut,Quatuor autum*

ni pleias orta facit,Autumno enimexiftenteib*

lein fcorpione,pleiade in tauro,eanon prius q*

riripoteft,quamfoloccidat.Etillud >TuncnoxThelTalicas urgebat paruafagittas. Parusc

<ftes,non nifigftatefuntDeindene^noxurget

fyderaadortum prius,quam ibloccidatSagits

tario autem, opponunturgemini, Ergo fole oc

cidentein geminis,iagittarius oriri iiibhoctem

pore alia ratione,quam acrony&enon potefL

Hanc uocem corruptaminchronicum libello

rioftro deSapheaadmonuimusJidemortus et

occafusapudauthores fepe miicentur:ficutfu*

perioriexemplo pleiademunotempore autumniOuidius oriri}uerum abfcondi dixitVergili

us.Sed

71 CANONICA SPHAERAB.

us. Sedhaxuarietas ledoremnon moret,qirin

aduertat tempus, quod poeta utercpdefignat:

pofteacondpiat locumfolis fuperechpricafub

idemtempus, deprehendetcpex infpe&ione 8i

motu fphgrae,quam fol diftan tia 3fiue aliqua, iis

ue nulla habeatadconceptu iydus.Secundum

ifta quifcpapud femet ftatuet,pro fuperioribus

definttionibus fenfum,adquem illi fuerintloi

quuti.Locum uero imaginisud ftelbefingula*

ris, qualem in fphaera habet, fi libucrit in ccclo

quocpdefignare,Corre&o fitu fph^rse,ad linea

cardinis admouebit quarta alterutrafuper ftel

lamin fph^ra. Index quoqjfuperquartam fta*

tuet in altitudinecontactus fte%,Secunduhoc

dirigat uifus,quapoteftfieri correftiffimepro

tndicationeindicisritautpereius^pceritatecon

tinuus radius perueniatad coclum. is perducct

adimagine &C ftellam cognatam:qu£quo cerri

or affumat, obferuet uicina cohors ftellarum,

quemadmodu huius afterifmus, configuratio

nem fimikmd cohorri in fph^rae aflumptae,

C XI.Dfe SIGNORVM ASCBNSlONliVS.

DVo circuli maximi in iphacra a?quator&ediptica, iugate afcendunt defcenduntqj

ad horizontem, (ednon paribus mutuo partii=

bus.Statuatenim exempLi caufa fignu G, edipti

caeinhorizonteapud R>& motufpheraecancer

totus afcendat in fuis partibus . Afcende*

runc

© R I 79

runtfimul gradusa£quatorisam,pfru$ *Statuat alterius exemplicauia fignumbrum^

,

in horizontem, &afcendat totus capricornus*

Afcenderunt intmmgradus^quatorisnon

t rgri xi i>Ad hsec exempla etiamin parti*

bus reliquis,drculus unus celerius tardius ueal

tero afcendit. H^c uero in^qualttas acciditedis

ptic£,non ^quatori,Aequatorenim fuper fuis,

&rjfdempolis mundi aequaliter mouet, ideft

paribustemporibusparesipfius arcusiemg a*

fcenduni, ficut idoftenfum cft capite de horis

diurnis.Sed ediptica,quiadiurna conuerfione

fertjtion fuper ^pprrj s fedmundi polis : ergo illi

cuenit in^qualitas afcenfionum,Eftergoafcen

fio figni autportionis ecliptic£, pars aequatoris

quscfimulafccndit Nunceiusafcenfionis ali*

quas dicemus ^prietates,&prioreloco uteue*

niuntfub fphgrarcdla,Ergo fiftamus eius utru

quepolum &C B^in fuperficiem horizonas a*

pudGgna & s. Quartae edipticse ordientes a

quatuorfignisc G d H,habentafcenfionesfuas

pares quartis affinibus ced

f

«cquatoris. oris

unturenim utrinq? pariteringradibusxc.Bii:

ni arcus ediptic£,& pares fibi,&:in diftantiapa

ri affumpti, ex aliquo quatuor iignorumccdhabent afcenfionespares:utarcus duogradu

umhinc l,& illinc toridem ex G figno, habent

afcenfiones uterq? pro fegraduu L 1 1 &:femis.

Nunc reuocemus iphseram fubdima Romai:

«· CAN0N1C SPHAER »

nu,quoniam tibi PauleBombafi deftinamus

comtrientarium hoc, qui Roma?,in hac luce or

bis terrarum manes beatus, Medietates duas

eclipticcC, hascc G D,illaD c5habent afcenfio

nes fuas pares affinibus medietadbus scquato

ris. finiuntenim pariter gradibus c 1 .Arcusectiptic£ quicunqueaiTumptusin medieta

te c G D,habet afcenfiones fuas maiores arcu af

fim gquatoristut arcus ecliptic£ ex c graduumxl v,habetpartes xquatoris coorientes rj*

Idem arcus habet afcenfiones fuas in fphsera

obliqua, minores iliis fuis in fpha?ra rc<f5a,ut

cumeodemarcu 1, cooriuntur in fph^rare:

d:agradus acquatoris l rj. Arcus eclipticacqui

cmiqueaflumptusin medietateD c,habet a*

fcenfionesfuasminores his affinibus axjuatos

ris, ut arcus ex d graduum 1 , habet afcenfi

onem ^quatoris afFinis graduu c I. Idem ar

cushabec afceniiones fuas maioresillis iphgis

ra refta, utcum eodem arcu lxxv, graduumCQoriunturitifphaera re&a gradus aequatoris

Ixxrj.Secundum haec dicamus proprietates,

qu^ communitereueniunt utriquefph^ra?. Arcus eclipticacaflumptus a quocunque initio&fine, afceniio eius eft portio a^quatoris, qusefis

mulafcendit fupra horizontem:utfigni tauri

afceniio fphsera re&a,eftgradusa:quatoris

x,etfcmis:in climateRomano gradus £qua

atoris i,Afcenfio cuiuflibet arcus diuidahir

per

R ! . 9

perxv-exibithora&pars perquantu tempusarcusdeeclipticaaiTumptus afcendit,uttaurus

ad ^ximumexemplu afcendithorauna&minus iemis, Arcus duo eclipticaeoppofiti ex diametrohabent inakerutralph^raafcenfiones fu

as iunftas,paresafcenfionibus iundisjquas in

alterahabent,utcanccr&capricornus in fphae

rare&a habetuterque pro fegradus rj.qui

iundi faciunt graduslxiiii . Cancerin clinia*

teRomano habet aicenfionemgradusxxxv.etfemis. Capricornusgradus ^quatoris

& femis , qui iun&i reddunt gradus»Omnia pun&a cum gradus in echptica, tumftellce fingulas habent afcenfionem fingularia

punda sequatoris, quas fimul in horizontemueniumt&C horum denominatio eft quanta,

&C eftipforum diftantiafupersequatoreex c fodhone uerna. Inde concipiuntur afcenfiones

reCtx fingularium pun&orum in coelo, qua*rum in prioribus fub ftellis infcribendis&condpiendis horis fecimus tam frequentem menrionem. Signumoriri recftedicitur

3qiio cummaior pars ^quatoris cooritunitaquefex fignamedietatis g d re&e oriuntur in fphgradecliui,

Signum oriri oblique dicitur,quocum

minor pars quatoris peroritur,

ut figna fexmedieta

tis C G.

1 C

«« CANONICA S AE

C XII,D S SIGNORVM DESCENSlONlBV S*

COmpertum ha&enus alrjs exemplu eft,

ut dierumet no&ium magnitudine,incp

sequidiftantium emerfu&occultatione, quodquaecunqueex diametro fphgrae opponuntur,

habeant apparentias comutatasteadem ratio*

nenuncquoc^quae recfte afcenduntfigna,ea^

dem defcendun tfecundu rationem,qua afceni

dutit iigna oppoiita,ex diametro uidelicet obli

que, utcancer defcenditquomodo afcendit ca^

pricornuSj nempe oblique: uiciffim capricors

nus defcendit,quomodoafcendit cancer, nempere&e, Hoc fitexemplum unum pro omnis

bus, unde intelligat qii£ fuperius de afcenfioni

bus dida funt, eadem did de defcenfionibus,

rationibuscomutatis.quare expofitione hanc

ad fuperiorem rerjdmus, Totaautem tractatio

afcenfionum defcenfionumque/ufripiturredi

dendae rarionis caufa diei diuerfa?,(iueapparen

risjfiueamfidalisjdieiquemcdiocris^ue^quai

lis:qii3c confideratio eft perneceiTariacomputa

ti nibus aftronomicis.D ei deu tcompertum

fieret,quomodo fex figna eclipticscxque emer*

gant fuprahorizontem,dielongiffimo& bre*

uiiTimo: fexqj defcendantno&e seque longiili

maatquebreuiffima^Quscuidffitudo&fupes

riora omniacolligens, iic exprefla eftcarmine

Vergiliano: Reda meant, obliquacadunt,a iy

R I .derecancri:Donec finitchyron

5fedacteraijg*

naNafcuntprono, defcendunt tramite refto.

C XIII.R C V R , F I G V R C L .

ELigaturftella aliqua inGgnis exacronydeoricnribus.huius notet afccnfio re&a.tunc

obferuata alritudine& uerticali, fubhorum comunemfedfaoncm ftatuat fteUa-Sph^ra fic cor*re&a^flumat fuper sequatorein hemifphscriononapparenri afcenfio re&agradusfolis. Hicipfeeft in horis nocfhirnisad prafens momen*tum^Bfteodemopereconftitutafiguraccelifei

cufidum orien ria&occidentia figna, ficut alio

capitecomemoratumeft, Altitudinem conue*niatconcipereextrinfecusperquadranterquoi

niam oculus obferuan tis non poteft fubirein*

terfphacram& quartam uerticatis, unde ueni*retutfus pergradus pares quarta^adfuperfici*

cm coeli ftell^uerticalis autem percommodeaccipitur uidelicet indextransfert ad quartamoppoiitam,perfummitatem eiusindiris etmesdium axem uerrids tranfmitrituruifus,&apprehenditcentrum ftellsc, &C notantur gradushorizontis, quibus diftat quartaexalteropimdo uel s meridian!,quod fitamborumpropius.Efto uero exempli cauia ex s.ergo quarta al

tera,qiiceeft e regioneftellscftatuat in totickmgradus ex m.Hocopereea quarta ftatin uertica

li ftdfehgc ergo fub eam admoueatur>etpr^fi*l * xaeft

f4 C . SPHAERAE R»

xaeftfiguracoeliadmomentum hoc obferua*

tionis. ergo afcenfio re&a folis notat eius pofiri

onem in horis,Hacratione,utfph^ra tamen fit

collata ad habitudinem climatis, fieri poteftob

feruatio per uerticalem foliim, ut non opus fit

altimdineconcipiendsL

C XII

DB DIST RBCTA t R V

flellarum in cceio,©- bhorum locorum in terra

,

Slnt ftelke in ccelo, imelocaduo infcripta in

fpha?rafecundum ^pprias radices. Tunc aUterum fiuelocum,fiue ftellam reuocemus iubVuerticem ,

per alterum punftum extendamus

quartam uerticalis,Gradus huius compreheru

fi inter uerticem&notam fecunda (untquse*

fitadiftantiare&a,Eftoexemplumperlocaduo

aflumpta. Romae radix longitudo fes

re,lautudo xlfj fere. Conftantinopolis radix

longitudo l i, latitudo prope 1. Diftanaa

comperiturfupercircunferenria quarta? gradu

umxx. reddunt in fuperfide terra? fecundum

diftantias notas nobis mccm paiTuu, qualium

1 M.paiTuum refpondentgradui unu

Totaoperado cixlitus apparenriu rerum,quatf

ta.puenitex motu a?quali ccefijttansfcrri huc

potuitrfed quoniaad comentatione Pliniana

feffinamus, qusc nos in rcliquaplura uocabir,

illucrcrjcimus 3quxhicpluradidpotuerunt»

I a

HEMICYCLI-V BEROSI, EX IACOBI

Ziegleri Landaui traditione.

Emicyclrj memiriit Vitruuius libro·emicyclium( quit)excauatuexqua

drato, ad enclimacp fiicdiiim. Berofus

Chaldseus didturinueniffeJftudego cumpropter Berofi nobilitatem, tumhunc Vitruui] lo

cum illuftrandum tradereinftitui.Defcribatur

in abaco linea c eius medium pundium ·.

unde educatur gpendkularistanquamaequas

toris iemidiameter, D,exhac refecetur proe

ceritas indicis.indeeijdat rciia F,fquidiftans

ipfi A,etcentroE,deiaib^turquartacoluriibl

ftitiorum,contingens figna fd, exD iumatur

arcus d diftantia tropica, item ex ueniat

gpendicularisH G,iuperD E,8icentro G.diftan

tiaautem fcribaturfemicirculus , is diuida

turin partessequasiex, S^pofitaregulafuperbi

nas fimiles partes sequidiftantes G,^tentur feftiones in arcu D H. pereas 8C centru

exeant rafcefuper c extrema, quseper hoteturfigno ueftBL totalatitudo conceptihemi

cyclfj Definienda etiam eft Iongitudo ex afc

fumptamenfura fciotheris E.is diuidat in par

tes aequas tres.ddnde extriniecus in abaco du*

I catur

U BEMlCVCLiVMturlinea. fupereaaiTumamur partes iex£quila*

tationis . quibus adrjdat ipfius una trium,

&finesnotentur fignis Bihseceftrata longie

tudo. diuidat in partes acquas iirj.Demurn

apteturlaminaacreacraffa^perpolitajficqjine

argentetur, ficnt defignariones in ea>&umbr*

multo illuftriores. Perhuius totam longitudi*

nemducaturmedialineaA c.ieceturmedia in

B, indeque educatur gpendicularis dbe. Poftaccipiatur diftantia l in fuperiori fchcma te5et

cransferatur in laminam ex uerfus d &e, fic

transferantur reliqua punda;hoc, proximumipfi

/

£ R S I

L,altmimj>ximu .Exhisfe&ionibus dti*

cant ^quidiftantes i ipfi c.earum denominatiointerimdifferatur, Pofh'd5exfectionibus

iirj.fuper linea altera acdpiat extenfio us

nius talium}etcum ea^quilatationediuidant fe

cundutotam longitudine^quidiftantes du£exL diftantia duda?, fado utrinqj inido exDB

E.iecundu idconcipiatpercanonica operatio^

neGue iapheg, fiue fphp-se apudProclum quatitas diurna diei folfticialis

5in horis& partibus

scquinodialibus in climate fufcepto, Sithgc excmpli caufahorarux v.ergo fuper unadiuifiu

rum,fumant utrinq? ex linead be fediones r)

ctiemis,Sdnotentfines^fimiliteraflumatquanstitas diurna diei brumehorgix,pro exemplo iii

periori;&exeademlineaD fumantutrincgi

fuperreliquadiWapartcsni)€tfemis.Binifines

hinc&hincexD EaffumptMungantredauenienteobliqpfuper^quidiftantes c.Hghabentraaonemportiohumhorizontisjquan

tumipfius comprehenditur a tota declinatios

ne edipticx apudfigna orientis &ocdden tis.

Tandem punfla fimilia fuper aequidiftanti*

bus iunganturredis paraUelisipfimedi£ dbe,Superetiamportionibus horizontis refecetur

tota exterior longitudo metalli* fuperfupres

rao margineporrionuhorizonasicribanf in*

dicia fignorum zodiaci, fuper c hic , illic

^fuperjplixiore& fuperbreuiore^>J& iiiper

reliquis

#9 h I C V C l l V

reliquisjfignareliquaad priorum ordinem.Ca

ftigeturquoqueiatitudo iaminseuidelicetjlinei

is cancri 8£capricorni, ducantcxtriniecus ^qui

diftanteSjfuperhisrefecenturexterioralaminaE?,

Bafis dicetur,ubi caricer ftatuaturlaminainba

fim. linea media dbe infcribit fj,quscad dexs

tram contratuentis I ,qu£ad iiniftram i,Sic fe*

quentes reliqu^ ex ordineharum deicriben tur,

Fa&is his neceflari]s deflgnationibus, reducat

lamina ad abfolutam rotunditatem, hoc eft he*

micyclium Berofi, addaturgnomon.isaflumatur paripfi E,undeueneruntex quarta F DparalldannterB Ljfigaturadangulos recflos fugs

ficid hemicydrj in comuni fedioneB.Huius examen eft,fuperduas fe&iones lineg &^cumhorizonte utrinque extendat regulaad huius

lineam, quarper medias fe&iones gtingat fummus apcx iiidicistdeinde fuperharumcommuni feftione, aiTumat di ftantia a?qua interutrua

quc fines fupcrhonsonte. fic index corre&us

firmctur . taridem fitlatur hemicydium faper

quadrato ad enclima fucdia Eius rei cauia ita*

tuaturdimaad quodhums ufum paratumuolumus.Eii:o iftud fecundum radonem prolixi*

tatem d/eram prius afTumpta graduum 1

.

acdpiaf tn quadrame fupenori f d, parar

cus d L5&;iunganiur redis F l,&e L,re<?k>an2

gulo ex'iitenteF,efl cuncus efl norma,fecun*

dumquam quadratu ad enclima fuccifum cor*

* fe R 9 1 ^rigatur.Eicuneo paretur extrinfccus in mateiria folida triangulus, par fecundum latera F,

quae bafis F L,qm' cathetus5& l E

3qugfubtenfarecflo didtur:dcmum ftatuat quadratu didumfuperius,qui fitperfedus cubus

3magnitudiniseius

5utlargecapiatambitumhemicydi].huius

hafis fit p!anum3huic cquidiftans B,Atfrons

notetur c> poftica D,iatera unum e> aiterum f,

omnia figna in medrjs umbilids fupcrficicaimper eas medias fuper medi]s fignis c D,diiscanturquatuorrc&£ fe femutuo periiimma capita exdpientibus.haec uno nomine dicetur \u

neacardtnis,Bafidusquadratiftanti in plani*degquali

3aptetfecundum iatera &TF5triangu

lum l F5 fic utbafis F

3bafi cubi in una plani*

dereipondeatAnguIus autemE3in angulum

fummum conueniat3hic ubi tres iugficks con*

curruntlaterisjpofticse& bafis.ffc aptato trian

gulo,ducaturperplanaE&Fcubi linea L.Secundumhasutrinquelineas

5refeceturquadrai:

tum fuperrefiduo ad baiim :ducaturpermcdUam planidem decliuem lineacardinis ex Rnubus qnxexA&D ad margines perueniun t.fiu

peream mediam efjdatur ppendicularis fuperlatera F, d dediui fuperficieifucdfequead erudimaimponaturhemicydium

5 ficutfedionesheg:hor£ ij 3reftemftentfug lineacardinis

3 itta3

uero ex i utrincpfuperorthogonali: index uero exeat re&us fuperreliquapartecardinis. Sic

1 QOXa

correftumhemicyclium confirmetur. Vfus ei*

us fciotherici eft, utlineaipfius cardinis itatua*

tur iti plahicie,in lineam eius nominis duftam,

in plancieadartificium 5quod defcribit Vitrutf

uius libro primo. Fronsautemc,refpidatautf

ftrum. Hscc ita perftringere breuiteruoluimus,

&nemuitadefiderentur}adiunximus fchema,

quo reliquaexemplo repraefentemus.

F I I S»

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