Cardano, Girolamo
,
De subtilitate
,
1663
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<
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id
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s.002661
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<
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Tria quæ ne
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ceſſaria ſunt
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ad viſus ra
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tionem aſſe
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quendam.</
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<
s
id
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s.002662
">Hoc enim modo haud difficile eſt cau
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ſam cognoſcere, cur aſtra, cùm plana
<
expan
abbr
="
videã-tur
">videan
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tur</
expan
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, ſint tamen rotunda: nam linea quæ à
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puncto D ad A oculum dirigitur, non eſt
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minor linea BA, nec CA, niſi in vna linea,
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quæ minor eſt DE: eò fit vt cùm linea DE,
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nullam habeat comparationem ad DA,
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propter nimiam aſtrorum altitudinem, igi
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tur non percipitur differentia vlla inter
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AB, & AC, & AD, quare omnes vi
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debuntur ab eodem plano erigi, igitur B
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DC videbitur plana, omnia igitur rotunda
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procul plana videbuntur. </
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id
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type
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<
s
id
="
s.002663
">Eſſe autem aſtara maxima, generaliter
<
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/>
nunc oſtendatur, & quòd maximè diſtent
<
lb
/>
<
arrow.to.target
n
="
marg298
"/>
<
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/>
primò, inde quòd ſint maxima. </
s
>
<
s
id
="
s.002664
">Cùm igi
<
lb
/>
tur duæ lineæ AB, & AC, producuntur ab
<
lb
/>
eodem puncto A, & ipſæ ſunt æquales, &
<
lb
/>
ſecantur duæ æquales FB, & FD, & duæ il
<
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lis etiam æquales GE, & GC, & ductæ
<
lb
/>
fuerint BC & FG, & perpendiculares DH,
<
lb
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EK, FL, & GM, erunt anguli L & H
<
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/>
æquales, quia recti, item BFL, & FDH, eò
<
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/>
quòd D H & FL, æquidiſtant, & linea DF,
<
lb
/>
recto oppoſita æqualis FB, oppoſitæ recto,
<
lb
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quare BL, æqualis FH, & MC, æqualis
<
lb
/>
KG eadem ratione. </
s
>
<
s
id
="
s.002665
">Sic igitur cùm BD ſit
<
lb
/>
maior FG, vt palam eſt ex quarta ſexti ele
<
lb
/>
mentorum Euclidis, erit vt BC poſſit augeri
<
lb
/>
tantùm, vt BL, & MC, quæ ſemper æqua
<
lb
/>
les manent, ſint minores in comparatione
<
lb
/>
diſtantiæ, data minima quantitate: igitur
<
lb
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tunc ex tertio ſuppoſito latente differentia
<
lb
/>
FB, & GC, vt æquidiſtantes habebuntur.
<
lb
/>
</
s
>
<
s
id
="
s.002666
">Hanc conatus eſt Vitellio oſtendere, quàm
<
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/>
non declarauit, multiſque tandem erroribus
<
lb
/>
admiſſis, quòd falſum oſtendere conatus eſt,
<
lb
/>
ſcilicet quòd BL eſſet minor FH: hoc au
<
lb
/>
tem falſum eſt: eſt enim, vt demonſtraui, æ
<
lb
/>
qualis, & ex hac æqualitate minorem ha
<
lb
/>
bet rationem ad BC ipſa BL, quàm FH ad
<
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/>
FG. </
s
>
<
s
id
="
s.002667
">Et hoc ſufficit ad propoſitum demon
<
lb
/>
ſtrandum. </
s
>
<
s
id
="
s.002668
">Cùm igitur Sol aut Luna, aut
<
lb
/>
aſtrum aliud vmbram faciat fermè æqua
<
lb
/>
lem in terra rei quæ videtur, aut ligno
<
lb
/>
quod radiis illius opponitur, ſeu ex vno
<
lb
/>
puncto radij procedant, ſeu ex toto corpo
<
lb
/>
re, permutata hac demonſtratione, conſtat
<
lb
/>
altitudinis ad FG proportionem eſſe in
<
lb
/>
comparabilem. </
s
>
<
s
id
="
s.002669
">Cùm hoc igitur contingat
<
lb
/>
etiam in turribus & montibus maximis, ne
<
lb
/>
ceſſe eſt, vt lineæ FB & GC ſint æquidi
<
lb
/>
ſtantes: quare altitudo A aſtri maxima,
<
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/>
<
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n
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<
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maximum igitur etiam aſtrum quod tam
<
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/>
procul ſub illa magnitudine, quam videmus,
<
lb
/>
cernitur. </
s
>
<
s
id
="
s.002670
">Eſt autem deducta ratione ex vm
<
lb
/>
bra terræ in deliquiis Solis, dimetiens ex
<
lb
/>
his partibus, quibus rerræ dimetiens eſt duo,
<
lb
/>
vndecim: quare cùm terræ dimetiens ſit bis
<
lb
/>
quinque millia paſſuum, erit Solis dime
<
lb
/>
tiens vndecies quinque millia paſſuum, id
<
lb
/>
eſt, paſſus millies quinquagintaquinque
<
lb
/>
millia. </
s
>
<
s
id
="
s.002671
">Solis autem corpus ad terram pro
<
lb
/>
portionem habet, quam quæ 166. & tres ex
<
lb
/>
octo partibus ad vnum, ambitus maioris
<
lb
/>
circuli M. paſſuum 173000. inſuperque 250.
<
lb
/>
Terræ dimetiens ad Lunæ dimetientem, quę
<
lb
/>
eſt 17. ad 5. ratio: itaque terræ corpus Lu
<
lb
/>
næ corpus continet fermè trigeſies nouies,
<
lb
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ac inſuper duas tertias. </
s
>
<
s
id
="
s.002672
">Lunæ dimetiens paſ
<
lb
/>
ſuum millia 2941. ambitus maioris circuli
<
lb
/>
<
expan
abbr
="
paſſuũ
">paſſuum</
expan
>
milia, 9000. & inſuper 264. Altitudo
<
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/>
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n
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<
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etiam horum ex Ptolemæi demonſtratione
<
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/>
habita talis eſt. </
s
>
<
s
id
="
s.002673
">Solis quidem à terræ cen
<
lb
/>
tro M. paſſuum ſexies mille M. & inſuper
<
lb
/>
quingenta. </
s
>
<
s
id
="
s.002674
">Lunæ verò ab eodem centro
<
lb
/>
M. paſſuum trecenta viginti M. & inſuper
<
lb
/>
833. Coni autem vmbræ ab eodem M. paſ
<
lb
/>
ſuum millies trecenties quadraginta M. </
s
>
<
s
id
="
s.002675
">Vn
<
lb
/>
de deductis M. paſſuum quinquies mille pro
<
lb
/>
ſemidiametro terræ à ſingulis harum di
<
lb
/>
ſtantiarum, relinquentur diſtantiæ Solis ac
<
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/>
Lunæ, necnon coni vmbræ à ſuperficie ter
<
lb
/>
ræ, ſeu ab oculis noſtris. </
s
>
<
s
id
="
s.002676
">Diſtantia etiam
<
lb
/>
Solis à Luna, quando Sol deliquium pati
<
lb
/>
tur, ſeu meliùs orbis ſolaris à Lunari orbe,
<
lb
/>
erit mille paſſuum Italicorum
<
emph
type
="
italics
"/>
(
<
emph.end
type
="
italics
"/>
nam de his
<
lb
/>
ſermo eſt) quinquies mille ſexcenties octua
<
lb
/>
ginta quatuor millia atque inſuper 167. Il
<
lb
/>
lud verò mirum quod Philippus Melanthon
<
lb
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animaduertiſſe videtur: quòd cùm eccentri
<
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Solis centrum Ptolemæi atque Hipparchi
<
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ætate diſtaret à terræ centro diametris terræ
<
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24. cùm quinta parte, ſeu M. paſſuum
<
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242000. nunc ſolùm diſtet diametris terræ
<
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<
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n
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decem & octo, duabuſque partibus ex quin
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que ſeu mille paſſuum centum octuaginta
<
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quatuor millia ab eodem terræ centro. </
s
>
<
s
id
="
s.002677
">Ar
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gumentum quaſi ſeneſcentis mundi. </
s
>
<
s
id
="
s.002678
">Sed
<
lb
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ratio deduci poteſt, vel ab inſtrumento
<
lb
/>
rum varietate, vel cœli ſolaris diſpoſitio
<
lb
/>
ne, vel æquinoctiorum obſeruatione, quæ
<
lb
/>
varietatem ſuſcipit & à locis, & à Solis
<
lb
/>
magnitudine, propter quam æquino
<
lb
/>
ctium aliquanto clariùs fit, quàm exiſti
<
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/>
metur. </
s
>
<
s
id
="
s.002679
">Hoc autem cùm obſeruatum eſſet
<
lb
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à multis, in Solis magnitudinem rela
<
lb
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tum eſt. </
s
>
<
s
id
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">Sol igitur A B, centrum eius
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<
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C, terra DE, centrum eius F, linea
<
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CHM, contingens Solem & terram, co
<
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nus M. </
s
>
<
s
id
="
s.002681
">Quoniam igitur GH contingit So
<
lb
/>
lem & terram, erunt anguli G & H recti,
<
lb
/>
quare GC, æquidiſtans FH, & ideò portio
<
lb
/>
GB, ſimilis portioni HE. </
s
>
<
s
id
="
s.002682
">Si igitur CG, ad
<
lb
/>
FH, proportio cognita eſt: erit & GM, ad
<
lb
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MH, qualis CM, ad MF. </
s
>
<
s
id
="
s.002683
">Et quia CM, </
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>
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