Cardano, Girolamo
,
De subtilitate
,
1663
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diſtantiam cognitus: quare angulus DCF,
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& F rectus eſt: igitur trigonus C F D co
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gnitus ex tabula de chorda, & arcu. </
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<
s
id
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s.003025
">Du
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cemus igitur C E H, & erit arcus B H ex
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planiſphærio illicò notus: nam hæc eſt pri
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ma operatio, & facillima illius inſtrumen
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ti, quæ illicò nobis occurrit. </
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<
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id
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">Igitur an
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gulus BCH notus: & eodem modo CFE re
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ctus: igitur trigonus CFE, & proportio quin
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que linearum CD, CE, CF, DE, EF, & quan
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ta ſit portio ſemicirculi EG ex tabula de chor
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da, & arcu: nam poſita DE, 60. duplicabi FG,
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quam infrà docebo, & arcus illi chordæ è
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directo ſcriptus, eſt totius iridis, quæ ap
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paret, id eſt, dupli G E. </
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<
s
id
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s.003027
">Et ita habes iam
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quantitatem iridis, quamuis non videas
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imum illius, id eſt, punctum G, nam vix
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vnquam poteſt eſſe certus de puncto G, an
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ſit ima pars iridis, propter locorum inæ
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qualitatem. </
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<
s
id
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s.003028
">Pòſt procedo ad L, & video
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altitudinem B M per E punctum, igitur
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angulus M E H eſt cognitus: quia ( vt de
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claratum eſt
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)
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vapores parum aſcendunt, ſed
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longè minus nubes: vt Albertus Magnus
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exiſtimat, non plus 15. ſtadiis: eſt igitur
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ac ſi angulus HCM eſſet in centro terræ,
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& ideò CEL cognitus, & F C E fuit co
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gnitus igitur C L E & totus trigonus
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C E L per eandem tabulam: & quia an
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gulus F E C cognitus fuit, & LEC, erit
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angulus FEL cognitus, quare cum F rectus
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ſit, erit trigonus FCL cognitus: quare pro
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portio FL ad LE cognita, & iam L E ad
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LC cognita fuit ex trigono ELC, igitur
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ratio FL ad L C cognita: ſed L C eſt co
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gnita menſura, eſt enim proceſſus tuus, igi
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tur FL cognita, & etiam FC ex ipſis com
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poſita: F G autem cognita fuit & ED: ideò
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cum duxeris EF in aggregatum ex E D &
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D E & producti latus quadratum acce
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peris, habebis G F ex S. ſexti, & 31.
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tertij elementorum Euclidis. </
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<
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id
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s.003029
">Ducta igi
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tur C F in ſe, & F G in ſe, latus ag
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gregati, eſt linea C G diſtantia à loco
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iridis, vbi terram tangit. </
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<
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id
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s.003030
">Conſpicuum
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autem eſt, quòd ſi quis ſuper montem
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aſcendat altiſſimum, iridem maiorem ſe
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micirculo videbit, & eò maiorem, quò
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mons altior extiterit: quod enim ha
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bet ante oculos ſpatium, vacui habet
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rationem Neque ignorare decet, maxi
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mam iridem non vltra quadraginta duas
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partes in noſtris regionibus ſupra finito
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rem eleuari. </
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<
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id
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">Maxima autem fit iris,
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quum Sol in occaſu, vel ortu extite
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rit, & linea C F fuerit longiſſima. </
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<
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id
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">Con
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ſtat igitur etiam ſciri poſſe, quanta ſit
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maxima iridis à nobis diſtantia, illius
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ſuppoſita magnitudine, tum verò ex di
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ſtantia ipſa magnitudinem, provt defi
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nitum eſt, comparata F G linea ad C G
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iam cognitam. </
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<
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id
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s.003033
">Iam verò ex reflexione
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conſtat, quòd ſi ſpeculum ponatur ſub
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aqua, imago Solis ab aqua reflectetur,
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quæ Solem referet alia verò quæ ex a
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quæ ſuperficie coanguſtatur ob medij den
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ſitatem, à ſpeculo reflectetur, & ſy
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deris exigui imaginem refert, putant
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que homines ſydus aliquod eſſe Soli pro
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pinquum, quod eo artificio detegatur,
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cùm ſatis conſtet imaginem eſſe Solis,
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ſed ab aqua in ſpeculum refractam, quam
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plerumque in deliquiis Solis homines, dum
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deliquium ſpectare ſtudent, in ſpeculo vide
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re ſolent.
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Quomodo di
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ſtantiam iri
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dis à noſtris
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pedibus de
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præhenda
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mus, & illius
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<
expan
abbr
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quãtitatem
">quantitatem</
expan
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.</
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Quomodo iris
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maxima poſ
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ſit videri.
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<
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<
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Quãtum
">Quantum</
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ſu
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pra
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finitorẽ
">finitorem</
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>
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eleuari poſſit
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iris.</
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in
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aqua ob ſpe
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culum.</
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<
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Cur dum Sol
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deliquum pa
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titur, figura
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per angulare
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foramen ra
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diorum
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abbr
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trã-ſeuntium
">tran
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ſeuntium</
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na
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uis formam
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referat.</
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Cur radij
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per
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abbr
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inciſurã
">inciſuram</
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angularem
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tranſeuntes,
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in ſubiectum
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planum ro
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tundam fi
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guram effin
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gant.</
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<
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id
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">Sed cur dum Sol deliquium pati
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tur, illius imago per angulare foramen
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delata, nauis formam refert? </
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<
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id
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">Mira nunc
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à me ratio radiorum eſt explicanda, ſed
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ſenſim ob difficultatem: nam cur pri
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mò radij per inciſuram angularem tran
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ſeuntes, in ſubiectum planum rotundam
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figuram, non rectam oſtendant, & eò
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rotundiorem, quò magis procul eſt pla
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num ab inciſura, demonſtrandum eſt.
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</
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<
s
id
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">Cauſa huius eſt duplex, quæ ſuperiùs
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eſt enarrata. </
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<
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id
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">Nam lineæ quæ priùs coi
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bant, quantò longiùs procedunt, tan
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tò æquidiſtantium magis naturæ appro
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pinquant: quò fit, vt ab angulorum na
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tura abſcedentes, rotundæ magis acce
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dant. </
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<
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id
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">Hoc igitur iam in ſuperiore figu
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ra demonſtrauimus: atque eò magis,
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quòd radij à toto Sole, non ab vno
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puncto prodeunt. </
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>
<
s
id
="
s.003045
">Altera eſt, quòd cùm
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figura quò magis abſcedit, eò magis au
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getur: oculus verò obiecti illam partem
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relinquit, quæ debilior eſt minima par
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te rei, quam videre poteſt, vt iam ſup
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poſuimus ab initio. </
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>
<
s
id
="
s.003046
">Cùm rotundior pars,
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& ampla, lumine ſuo angulos obum
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bret, neceſſe eſt, vt partes tenuiorum
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virium, id eſt, angulares, priùs mo
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uere viſum deſinant mediis, in quas co
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pioſus emittitur radius: igitur figuræ il
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læ rotundæ apparebunt, & eò rotundio
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res, quò magis non ſolum ab inciſura
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ea, per quam radij tranſeunt illam con
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ſtituentes abfuerint, ſed etiam ab ocu
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lis intuentium. </
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>
<
s
id
="
s.003047
">Hæc igitur cum ſint cla
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riſſima, & vbi lumen ſub propria qua
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ſi quantitate excipitur, ſi quid ſit inter
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medium, cum vmbra defertur: imagi
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ne igitur Solis quaſi ſub magnitudine
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redacta, quà ſubiicitur oculis inciſuræ
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beneficio, cum Luna interpoſita ſit cor
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pus denſum atque opacum, neceſſe eſt
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vmbram etiam Lunæ in figuræ videri.
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</
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<
s
id
="
s.003048
">Sed Lunæ vmbra rotunda eſt, quia Lu
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na ipſa eſt rotunda, & forma à qua ab
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ſcinditur rotunda: igitur cum à rotundo
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rotundum ex vna parte aufertur, relin
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quatur nauiculæ ſeu vacuæ Lunæ imago,
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neceſſe eſt in deliquiis formas, quæ in
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planis deſcribuntur, à radiis per angula
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res inciſuras tranſeuntibus, nec angula
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res nec rotundas eſſe, ſed lunares, ſeu
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ad nauiculæ formam factas. </
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>
<
s
id
="
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">Verum opus
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eſt diligenti conſpectu, quoniam cum
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Luna ſit peruia, rotunda videbitur eiuſ
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modi figura. </
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<
s
id
="
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">Sed clarior par lunarem for
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mam ( vt dixi ) repræſentat. </
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>
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<
s
id
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">Hæc volui ſubiicere, quoniam hoc in
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libro, vt præfatus ſum, nihil falſum, aut
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dubium ſcribere volui. </
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>
<
s
id
="
s.003052
">Quòd ſi cui ea, quæ
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proponimus, non ſuccedant, ſeipſum igno
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rantiæ, non me accuſet mendacij. </
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>
<
s
id
="
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">Sed ad
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rem regredior. </
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>
<
s
id
="
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">Eiuſdem deliquij tempore </
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