Cardano, Girolamo
,
De subtilitate
,
1663
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tendenti. </
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<
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s.002637
">Sit rurſus A oculus in aëre, B
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res viſa in aqua, perpendicularis ad aë
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rem BE, rectà BFA, inflectatur à perpen
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diculari ad oculum ex, F, vt fiat BFC, pro
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ducatur CF, in D, & B, videbitur in
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C, igitur aquæ altitudo videbitur ſolùm
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DE, Rurſus ſtella in cœlo D cœlum quic
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quid eſt ſupra EF, perpendicularis DE, ra
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dius qui directè procedit DFC, cùm per
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uenit ad F, medium denſius, id eſt, ad
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aërem, inflectitur verſus cathetum, ſitque
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DFA, per quem oculus A, videt D, ſtel
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lam: producatur ergo AF, directè, & vi
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debitur D in B, vbi ſcilicet concurrunt ca
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thetus DE, ex re viſa ad medium, & li
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nea B F A, cùm dirigitur à parte illa quæ
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ad oculum pertingit, id eſt, pars AF, ocu
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lum tangens.
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Res quæ vi
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detur vbi
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ſemper appa
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ret.</
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<
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Cur ſtellæ
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multò minus
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ſublimes iu
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dicentur
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quàm ſint.
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</
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<
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id
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">Sydera om
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nia cur in
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oriente & oc
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cidente, ma
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iora videan
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tur.</
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</
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<
s
id
="
s.002641
">At dices, ſtellæ multò propriùs videntur
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eſſe quàm ſint, ſi vera ſunt quæ Aſtrologi
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de illarum referunt altitudine: non igitur
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altiores eſſe videntur quàm ſint. </
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<
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id
="
s.002642
">Fateor lon
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gè eas propius exiſtimari: ſed alia cauſa, ea
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ſcilicet quòd medium ſpatium inter nos &
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illas non compræhenditur: ob id contra
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ria ratione aſtra omnia dum oriuntur &
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occidunt, maiora videntur, quàm in cœ
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li medio, quoniam terræ magnitudo in
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termedia facit, vt oculus ea plus diſtare
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exiſtimet, & ob id eſſe maiora: nam &
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turris vlna maior iudicatur ab oculo illius
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diſtantiam compræhendente, tametſi mino
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rem angulum in oculo faciat vlna ipſa. </
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>
<
s
id
="
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">Ob
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id igitur aſtra propinqua videntur quòd
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nullum eſt medium corpus inter ipſa &
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oculum, cuius longitudinem oculus depræ
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hendere poſſit, atque ob id ipſa exiſti
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mare procul abeſſe, quamvis ( vt dixi )
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medij ratio ea altiora oſtendat. </
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<
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id
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">Sed quòd
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ſtellæ in Oriente, & Occidente maiores
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videantur, facit & denſitas aëris, non in
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qua nos ſumus, ſed quæ procul à nobis
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eſt. </
s
>
<
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id
="
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">Argumento id eſſe debet, quòd nebu
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loſo tempore aſtra etiam longè maiora vi
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dentur. </
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<
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id
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">Hoc autem eſſe non poſſet, ſi ob ſo
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lam diſtantiam id contingeret. </
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<
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">Sed ad narrationem loci in quo res eſſe
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videtur, exemplis peruenio. </
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<
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id
="
s.002648
">Sit oculus A,
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res viſa B, ſpeculum CD, ducatur BF, per
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pendicularis ad ſuperficiem ſpeculi intelli
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gendo extenſam, non enim neceſſarium
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eſt, vt tangat, & ducatur BE, reflexa ad
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A, ita quòd angulus BEC ſit æqualis AED,
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hoc enim neceſſarium eſt in omni radij re
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flexione à ſpeculo cuiuſcunque generis: du
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cta igitur parte reflexa AE, concurrat in
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F, & ibi videbitur eſſe B, cui conſentit
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experimentum. </
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<
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id
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">In cauo etiam ſpeculo CD,
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cuius centrum E, res quæ videtur primò
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ponatur B, per radium reflexum BCA ad
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oculum, & manifeſtum eſt, quòd perpen
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dicularis erit BF, cui occurrat AC, reflexa
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in puncto F, & hîc erit locus vbi videbi
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tur ab oculo A eſſe B, res quæ videtur, quò
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fit vt non quemadmodum in priore figura
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B appareat in F, in directo ſui. </
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<
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">Hîc enim
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plerunque videbitur non in directo F, ip
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ſius B, eò quòd oculus iudicat ad compa
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rationem plani cuiuſdam D K, ſuperiacen
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tis ſpeculo, & tamen punctus F, & ca
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thetus ſumitur à puncto E, quem oculus
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nec videt, nec comprehendit. </
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<
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id
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">Sit rurſus
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G, quod videtur in cauo ſpeculo, & per
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pendicularis GEF, neceſſariò erit, & per
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GDA, reflexum radium videatur ab A ocu
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lo, igitur radius A D, occurret catheto in
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H: igitur res videbitur in H, & ita in aëre
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extra ſpeculum: & eſt mirabile, ſed con
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ſentit tamen experimento. </
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<
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id
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">Verùm longè
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meliùs in magnis ſpeculis hæc fieri vidi
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mus, vt prorſus ſit res miraculo ſimilis.
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</
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<
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id
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">Sed fit etiam in aliis ſpeculorum ſpeciebus
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velut conuexis, rotundis, ac columnari
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bus. </
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<
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">Additur miraculo maius miraculum,
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cùm res quæ non eſt in aëre videtur, dæ
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monum imitatione propoſita, vt Vi
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tellio docuit: cuius rationem inferius,
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dum de luce & lumine loquemur, expo
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nemus. </
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In cauis ſpe
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culis res ma
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gis latere
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videntur,
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quàm ſint
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plerumque.</
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Quomodo re
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imago è ſpe
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culo in aëre
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videatur.</
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Lib. 7. cap.
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vlt.</
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<
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id
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">Igitur vt ad vltimum genus perueniam,
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poſito rurſus conuexo ſpeculo CD, & ocu
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lo A, & B, re viſa, cathetus ad centrum ſpe
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culi BD GE, & illi occurrit radius refle
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xus AFC, in G, videbitur B. </
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>
<
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id
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">Eadem ratio
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in colùmnaribus & conicis locum rei viſæ
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oſtendit. </
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>
<
s
id
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">Iam ergo tria ſunt, quæ neceſſa
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ria ſunt ad viſum: locus rei viſæ, & vt res
<
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non ſit minor ea quæ minima eſt, quæ ſub
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ea diſtantia videre poteſt: eam enim in qua
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cunque diſtantia inueniri eſt neceſſarium,
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ſcilicet minimam, & quòd omnis res mini
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ma minor, eſt ac ſi non eſſet. </
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