Cardano, Girolamo
,
De subtilitate
,
1663
Text
Text Image
Image
XML
Thumbnail overview
Document information
None
Concordance
Figures
Thumbnails
List of thumbnails
<
1 - 10
11 - 20
21 - 30
31 - 40
41 - 50
51 - 60
61 - 70
71 - 80
81 - 90
91 - 100
101 - 110
111 - 120
121 - 130
131 - 140
141 - 150
151 - 160
161 - 170
171 - 180
181 - 190
191 - 200
201 - 210
211 - 220
221 - 230
231 - 240
241 - 250
251 - 260
261 - 270
271 - 280
281 - 290
291 - 300
301 - 310
311 - 320
321 - 330
331 - 340
341 - 350
351 - 360
361 - 370
371 - 380
381 - 390
391 - 400
401 - 403
>
81
82
83
84
85
86
87
88
89
90
<
1 - 10
11 - 20
21 - 30
31 - 40
41 - 50
51 - 60
61 - 70
71 - 80
81 - 90
91 - 100
101 - 110
111 - 120
121 - 130
131 - 140
141 - 150
151 - 160
161 - 170
171 - 180
181 - 190
191 - 200
201 - 210
211 - 220
221 - 230
231 - 240
241 - 250
251 - 260
261 - 270
271 - 280
281 - 290
291 - 300
301 - 310
311 - 320
321 - 330
331 - 340
341 - 350
351 - 360
361 - 370
371 - 380
381 - 390
391 - 400
401 - 403
>
page
|<
<
of 403
>
>|
<
archimedes
>
<
text
>
<
body
>
<
chap
>
<
p
type
="
main
">
<
s
id
="
s.003420
">
<
pb
pagenum
="
433
"
xlink:href
="
016/01/082.jpg
"/>
niam DBC, eſt rectus, & CBE, obtuſus. </
s
>
<
s
id
="
s.003421
">Ve
<
lb
/>
rùm de radiis alia eſt ratio: etenim illi motu
<
lb
/>
<
arrow.to.target
n
="
marg422
"/>
<
lb
/>
ſuo, angulum ſenſilem efficiunt in oculo,
<
lb
/>
ideóque moueri deberent videri. </
s
>
<
s
id
="
s.003422
">Cur autem
<
lb
/>
non videantur, cauſa hæc eſt, quia poſita ter
<
lb
/>
ra, cuius centrum A, & plano eius
<
emph
type
="
italics
"/>
(
<
emph.end
type
="
italics
"/>
vt dixi)
<
lb
/>
quod refert punctum D, ſed nobis ob ma
<
lb
/>
<
figure
id
="
id.016.01.082.1.jpg
"
xlink:href
="
016/01/082/1.jpg
"
number
="
61
"/>
<
lb
/>
gnitudinem eſt BC, & turris quæ ad perpen
<
lb
/>
diculum eſt ſuper planum DE, & Sole in F,
<
lb
/>
qui producens radium FEC, producit CD,
<
lb
/>
cum autem Sol proceſſerit in G, producto
<
lb
/>
radio GEK, relinquit vmbram KD, igitur
<
lb
/>
cùm motus indicetur ex vmbra, Sol videbi
<
lb
/>
tur ſolum pertranſiſſe ex C, in K, dum moue
<
lb
/>
tur ex F, in G: ſed ſpatium CK, eſt paruum,
<
lb
/>
cùm ſit comparatum ad altitudinem D E,
<
lb
/>
quæ eſt parua: igitur cum ſenſim moueatur,
<
lb
/>
& tranſeat ſolùm ſpatium CK, puta in quar
<
lb
/>
ta horæ ſingulo momento, nullum ſpatium
<
lb
/>
tranſibit quod angulum ſenſilem efficiat. </
s
>
<
s
id
="
s.003423
">Igi
<
lb
/>
tur videbitur ex illo ſuppoſito ſæpius repe
<
lb
/>
tito, radius FC,
<
expan
abbr
="
dũ
">dum</
expan
>
mouebitur ſemper quieſ
<
lb
/>
cere. </
s
>
<
s
id
="
s.003424
">Ponamus exemplum, cum Sol eſt in 7.
<
lb
/>
parte Tauri hora circiter 19. cum quarta,
<
lb
/>
vmbra æquatur gnomoni, 21. detracta quar
<
lb
/>
ta, dupla eſt: conduplicatur ergo vnius & di
<
lb
/>
midiæ horæ ſpatio. </
s
>
<
s
id
="
s.003425
">Ergo motus eſt iuxta gno
<
lb
/>
monis longitudinem, non Solis velocitatem.
<
lb
/>
</
s
>
<
s
id
="
s.003426
">Verum dices, cur non videtur moueri radius?
<
lb
/>
</
s
>
<
s
id
="
s.003427
">cauſam intelligo: quomodò verò tantum ſpa
<
lb
/>
tij ſuperet, nec moueri videatur, cauſam non
<
lb
/>
intelligo. </
s
>
<
s
id
="
s.003428
">Conſtat enim ſub ortu occaſu vm
<
lb
/>
bras velociſſimè maximiſque incrementis,
<
lb
/>
aut decrementis variati. </
s
>
<
s
id
="
s.003429
">Sit igitur Sol occi
<
lb
/>
<
figure
id
="
id.016.01.082.2.jpg
"
xlink:href
="
016/01/082/2.jpg
"
number
="
62
"/>
<
lb
/>
dens C, planum GE, corpus erectum AB, fi
<
lb
/>
nis vmbræ
<
emph
type
="
italics
"/>
(
<
emph.end
type
="
italics
"/>
qui idem eſt cum initio radio
<
lb
/>
rum) E, corpus aliud erectum EF: in quo mo
<
lb
/>
tus vmbræ inſenſilis ſit, quoniam ſolùm dum
<
lb
/>
Sol occidit radij deſinunt illuſtrare. </
s
>
<
s
id
="
s.003430
">Ipſi verò
<
lb
/>
clariſſimi erunt, quando angulus CEF, rectus
<
lb
/>
eſt. </
s
>
<
s
id
="
s.003431
">At ex puncto E, nulli dubium eſſe poteſt,
<
lb
/>
quin in plano GAE, tum radij, tum vmbra
<
lb
/>
prope Solis occaſum incredibili velocitate
<
lb
/>
ferantur,
<
expan
abbr
="
quãtum
">quantum</
expan
>
enim punctus in ſuperficie
<
lb
/>
terræ è regione centri Solis mouetur, tanto
<
lb
/>
magis neceſſe eſt vmbras promoueri. </
s
>
<
s
id
="
s.003432
">Sed
<
lb
/>
quoniam in priore figura, ſi F, ponatur in oc
<
lb
/>
caſu anguli FAE, FEA, erunt quaſi recti ob
<
lb
/>
paruitatem AE, & rationem trigonorum cir
<
lb
/>
culis inſcriptorum iuxta arcum & chordam,
<
lb
/>
vt vocant, erunt ergo anguli FC, lineæ, cum
<
lb
/>
duabus è centro A, exeuntibus ad illam al
<
lb
/>
teram, quarum eſt AD, altera velut AK, fer
<
lb
/>
mè recti: ergo vmbra quæ ſubtenditur quæ
<
lb
/>
que maxima eſt, minima eſt. </
s
>
<
s
id
="
s.003433
">Igitur non fiet
<
lb
/>
ille progreſſus maximus, niſi DE, fuerit lon
<
lb
/>
giſſima, quod eſſe non poteſt in comparatio
<
lb
/>
ne ad AD. </
s
>
<
s
id
="
s.003434
">Alia cauſa eſt, quoniam quantò
<
lb
/>
magis creſcit AE, eò radiorum vis minuitur
<
lb
/>
propter paruitatem anguli AEB: igitur nec
<
lb
/>
vmbra, nec radius dignoſcitur: quamobrem
<
lb
/>
in dubia luce, neque lux ipſa percipitur, ne
<
lb
/>
que multo minus vmbra quæ propter lucem
<
lb
/>
dignoſcitur, nec vmbræ magnitudo etiam
<
lb
/>
minus, nec tandem adhúcque minus vmbræ,
<
lb
/>
vel radiorum motus. </
s
>
<
s
id
="
s.003435
">Dices rurſus, quomodo
<
lb
/>
vmbra fiet infinita ſtatim ſi maxima parua
<
lb
/>
eſt? </
s
>
<
s
id
="
s.003436
">coniungitur illa vmbræ rotunditatis terrę
<
lb
/>
quæ maxima eſt, & ſic è parua fit infinita in
<
lb
/>
momento. </
s
>
<
s
id
="
s.003437
">Cùm verò nullum fuerit corpus in
<
lb
/>
plano, velociſſima fit & lucis & vmbrarum
<
lb
/>
diffuſio, ſed quia lux in vtroque crepuſculo
<
lb
/>
(vt ita dicam) dubia eſt, & ſpatium quod ab
<
lb
/>
oculo illuminatum videtur exiguum, ſtatim
<
lb
/>
vtraque facta mutatione latet motus, vt in
<
lb
/>
ſecunda cauſa demonſtratum eſt. </
s
>
</
p
>
<
p
type
="
margin
">
<
s
id
="
s.003438
">
<
margin.target
id
="
marg421
"/>
Propoſit. 13.</
s
>
</
p
>
<
p
type
="
margin
">
<
s
id
="
s.003439
">
<
margin.target
id
="
marg422
"/>
Cur ſolis ra
<
lb
/>
dij cum in
<
lb
/>
23. ſerie ter
<
lb
/>
ram circum
<
lb
/>
eant immo
<
lb
/>
biles vi
<
lb
/>
deantur.</
s
>
</
p
>
<
p
type
="
main
">
<
s
id
="
s.003440
">Dubium quoque eſt, cur hæc illuſtratio
<
lb
/>
<
arrow.to.target
n
="
marg423
"/>
<
lb
/>
in terra ſemper tremere videatur? </
s
>
<
s
id
="
s.003441
">& an ab
<
lb
/>
eorum quæ dicta ſunt aliquid? </
s
>
<
s
id
="
s.003442
">Cauſa igi
<
lb
/>
tur eſt, quòd mouetur, nec moueri videtur,
<
lb
/>
vt dictum eſt: medium igitur quippiam per
<
lb
/>
cipitur. </
s
>
<
s
id
="
s.003443
">Idem
<
expan
abbr
="
etiã
">etiam</
expan
>
& ex ambigua viſione, ter
<
lb
/>
minus enim vmbræ & luminis, neque vmbra
<
lb
/>
eſt neque lux, tremere autem exiſtimantur
<
lb
/>
quæcunque, an moueantur incertum eſt, hoc
<
lb
/>
autem ob cauſas dictas. </
s
>
<
s
id
="
s.003444
">Sed cur non in horo
<
lb
/>
logio index? </
s
>
<
s
id
="
s.003445
">Quoniam non eſt is motus ob
<
lb
/>
tarditatem vllo modo ſenſilis: quæ autem
<
lb
/>
tremere videntur, non adeò tardè moueri
<
lb
/>
oportet, vt omninò quieſcere videantur. </
s
>
</
p
>
<
p
type
="
margin
">
<
s
id
="
s.003446
">
<
margin.target
id
="
marg423
"/>
Cur ſolis il
<
lb
/>
luſtratio tre
<
lb
/>
mula videa
<
lb
/>
tur.</
s
>
</
p
>
<
p
type
="
main
">
<
s
id
="
s.003447
">His cognitis maius quippiam ſuccedit,
<
lb
/>
quo humana ſubtilitas altitudinem omnium
<
lb
/>
ſyderum tam facilè metiri docuit, vt nemo
<
lb
/>
tam in promptu domus ſuæ partes habeat.
<
lb
/>
</
s
>
<
s
id
="
s.003448
">Cum enim in figura motus Solis altitudo F,
<
lb
/>
nota fuerit, ſeu planiſphærio, ſeu armillis,
<
lb
/>
alióve inſtrumento, aut tabulis, ea detracta
<
lb
/>
ex 90. partibus habebimus angulum FAD,
<
lb
/>
ſed angulus CED, ratione & menſura notus
<
lb
/>
eſt, ſeu C, terminus ſit vmbræ, ſeu oculus: igi
<
lb
/>
<
arrow.to.target
n
="
marg424
"/>
<
lb
/>
tur angulus FEA, notus, quare ex traditis ab
<
lb
/>
Euclide in elementis, angulus F, & ratio FE,
<
lb
/>
altitudinis ad AE, dimidium dimetientis ter
<
lb
/>
ræ, quoſt ſuperius quantum eſſet, demonſtra
<
lb
/>
uimus. </
s
>
<
s
id
="
s.003449
">Eſt enim quinquies M. paſſ millia.
<
lb
/>
</
s
>
<
s
id
="
s.003450
">Virga autem DE, habere debet circulum in
<
lb
/>
imo chalybèum, cui inſiſtat orthogonia: tum
<
lb
/>
& planum ad vnguem inferna parte
<
expan
abbr
="
circulũ
">circulum</
expan
>
<
lb
/>
eſſe, vt cùm applicetur plano, intelligas an
<
lb
/>
illud verè planum ſit, habeat & ſuperius à
<
lb
/>
quatuor lateribus plumbea perpendicula: &
<
lb
/>
notæ ſit magnitudinis à ſummo verticis
<
expan
abbr
="
vſq;
">vſque</
expan
>
<
lb
/>
ad imam chalybei circuli ſuperficiem. </
s
>
<
s
id
="
s.003451
">Cùm
<
lb
/>
igitur virga fixa circulo tenus illóque hæren.
<
lb
/>
</
s
>
<
s
id
="
s.003452
">te vndequaque plano etiam perpendicula </
s
>
</
p
>
</
chap
>
</
body
>
</
text
>
</
archimedes
>