Cardano, Girolamo
,
De subtilitate
,
1663
Text
Text Image
Image
XML
Thumbnail overview
Document information
None
Concordance
Figures
Thumbnails
Page concordance
<
1 - 30
31 - 60
61 - 90
91 - 120
121 - 150
151 - 180
181 - 210
211 - 240
241 - 270
271 - 300
301 - 330
331 - 360
361 - 390
391 - 403
>
Scan
Original
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
<
1 - 30
31 - 60
61 - 90
91 - 120
121 - 150
151 - 180
181 - 210
211 - 240
241 - 270
271 - 300
301 - 330
331 - 360
361 - 390
391 - 403
>
page
|<
<
of 403
>
>|
<
archimedes
>
<
text
>
<
body
>
<
chap
>
<
pb
pagenum
="
589
"
xlink:href
="
016/01/236.jpg
"/>
<
p
type
="
main
">
<
s
id
="
s.010728
">Et rurſus, dum è dextra in ſiniſtram tendis,
<
lb
/>
hoc aliud in ſepto:
<
lb
/>
<
emph
type
="
quote
"/>
<
emph
type
="
italics
"/>
Magnus veſtit honor, latus loquor hoc nationi.
<
emph.end
type
="
italics
"/>
<
emph.end
type
="
quote
"/>
</
s
>
</
p
>
<
p
type
="
main
">
<
s
id
="
s.010729
">Simili curioſitate Plautus vſus eſt, in con
<
lb
/>
ſcribendo nomine, argumenti fabulæ per
<
lb
/>
capita dictionum, quæ in initio argumenti
<
lb
/>
ipſius fabulæ poſita ſunt, literas primas col
<
lb
/>
ligendo. </
s
>
<
s
id
="
s.010730
">Sed illa magis Comœdum decue
<
lb
/>
runt, quàm ſi ex compoſito, hanc ratio
<
lb
/>
nem totus ſe illi dedens iniſſet. </
s
>
<
s
id
="
s.010731
">Velut Hug
<
lb
/>
baldus Gallus, monachus Eluomenſis, ex or
<
lb
/>
dine beati Benedicti, qui centum triginta
<
lb
/>
ſex carminibus, quorum ſingulæ dictiones
<
lb
/>
elemento C, initium ſumebant, Laudes Ca
<
lb
/>
roli Calui Francorum Regis ſcripſit, quorum
<
lb
/>
initium eſt:
<
lb
/>
<
emph
type
="
quote
"/>
<
emph
type
="
italics
"/>
Carmina clariſona caluis cantate camœnæ.
<
emph.end
type
="
italics
"/>
<
emph.end
type
="
quote
"/>
</
s
>
</
p
>
<
p
type
="
main
">
<
s
id
="
s.010732
">Simili illud Placentij Porcij, qui Pu
<
lb
/>
gnam porcorum trecentis penè carmini
<
lb
/>
bus cecinit: quorum ſingulæ dictiones ex
<
lb
/>
P, littera initium ſumunt. </
s
>
<
s
id
="
s.010733
">Extat opus im
<
lb
/>
preſſum non inelegans, apud me: cuius ini
<
lb
/>
tium eſt:
<
lb
/>
<
emph
type
="
quote
"/>
<
emph
type
="
italics
"/>
Plandite porcelli, porcorum pigra propago.
<
emph.end
type
="
italics
"/>
<
emph.end
type
="
quote
"/>
</
s
>
</
p
>
<
p
type
="
main
">
<
s
id
="
s.010734
">Sed ſi hæc coniunctam in ſe habe rent
<
lb
/>
aliquam vtilitatem, ſumma dignum laude
<
lb
/>
hominem arbitrarer: nunc verò tam operam
<
lb
/>
irridere licet, quàm etiam ingenium admi
<
lb
/>
rari. </
s
>
<
s
id
="
s.010735
">Placere poteſt exemplum, copia horum
<
lb
/>
certè tædium parit. </
s
>
<
s
id
="
s.010736
">Hócque vnum fermè eſt
<
lb
/>
commune his, quorum nullus inter homines
<
lb
/>
vſus eſt. </
s
>
</
p
>
<
p
type
="
main
">
<
s
id
="
s.010737
">Atque hæc penè ſimilia induſtriæ egregij
<
lb
/>
illius viri, qui cicere, cùm quemcunque
<
lb
/>
vellet locum feriret, ciceris modium ab A
<
lb
/>
lexandro promeruit: magis auerſatus ina
<
lb
/>
nem laborem, quàm induſtriam admira
<
lb
/>
tus. </
s
>
<
s
id
="
s.010738
">Eiuſdem etiam, ſed aliquantò vtilio
<
lb
/>
ris argumenti ſunt libri illi quatuor Geo
<
lb
/>
<
arrow.to.target
n
="
marg1508
"/>
<
lb
/>
metrici Procli in Euclidis elementa: nihil
<
lb
/>
enim nouum docent, ob idque ad artem non
<
lb
/>
ſpectant. </
s
>
<
s
id
="
s.010739
">Quia tamen varia eſt ſubtilitas il
<
lb
/>
la, non vnius prorſus generis, vt in Rhabano
<
lb
/>
& Lullio, ideò non omninò vt inutiles abii
<
lb
/>
ci, & ſperni debent. </
s
>
<
s
id
="
s.010740
">Nam & ipſius ſubtilita
<
lb
/>
tis cùm plura fuerint exempla, ars quædam
<
lb
/>
etiam erit.
<
lb
/>
<
arrow.to.target
n
="
marg1509
"/>
</
s
>
</
p
>
<
p
type
="
margin
">
<
s
id
="
s.010741
">
<
margin.target
id
="
marg1508
"/>
Procli libri
<
lb
/>
non ſpectant
<
lb
/>
ad artem
<
lb
/>
<
expan
abbr
="
Geometricã
">Geometricam</
expan
>
.</
s
>
</
p
>
<
p
type
="
margin
">
<
s
id
="
s.010742
">
<
margin.target
id
="
marg1509
"/>
Quomodo
<
lb
/>
quæcunque
<
lb
/>
in elementis
<
lb
/>
Euclid. </
s
>
<
s
id
="
s.010743
">de
<
lb
/>
monſtrata
<
lb
/>
ſunt, abſque
<
lb
/>
vlla propoſi
<
lb
/>
ti vnius tan
<
lb
/>
tum circuli
<
lb
/>
mutatione
<
lb
/>
oſtendi poſ
<
lb
/>
ſint.</
s
>
</
p
>
<
p
type
="
main
">
<
s
id
="
s.010744
">Igitur conſimili argumento quale fuit
<
lb
/>
Procli, oſtentatione potius iuuenili, quàm
<
lb
/>
vtilitate manifeſta, tum ego, tum Ludo
<
lb
/>
uicus Ferrarius paucis in diebus inuenimus,
<
lb
/>
quónam pacto quæcunque ab Euclide de
<
lb
/>
monſtrantur, variata circini latitudine, à
<
lb
/>
nobis ſub quacunque latitudine illius à con
<
lb
/>
tradicente propoſita inuariabilique, præ
<
lb
/>
ter circulorum ſolam inſcriptionem ac cir
<
lb
/>
cumſcriptionem, perfectè à nobis poſſent
<
lb
/>
oſtendi. </
s
>
<
s
id
="
s.010745
">Et quamvis dum hæc ſcriberemus,
<
lb
/>
Ludouicus ipſe hanc totam demonſtratio
<
lb
/>
nem typis exceptam edidiſſet optimè, quia
<
lb
/>
tamen opus illud contentionis gratia ſcri
<
lb
/>
ptum eſt, haud arbitror ſuperfuturum, cùm
<
lb
/>
nihil aliud fermè egregij contineat: & ſi
<
lb
/>
quædam ſint egregia, ſeorſum tamen poſi
<
lb
/>
ta ſunt, & non vnius generis, ita poſtu
<
lb
/>
lante materia: quo fit vt operæ pretium eſſe
<
lb
/>
duxerim, ne quandoque tam rarum ſubtili
<
lb
/>
tatis exemplum periret, illud denuò hîc ſub
<
lb
/>
iicere. </
s
>
<
s
id
="
s.010746
">Sed quomodo? </
s
>
<
s
id
="
s.010747
">breuius demonſtratio
<
lb
/>
nibus: ne abhorrentes à Geometricis tædio
<
lb
/>
capiantur. </
s
>
</
p
>
<
p
type
="
main
">
<
s
id
="
s.010748
">Igitur primò, quarta primi Elemento
<
arrow.to.target
n
="
marg1510
"/>
<
lb
/>
rum, velut ab Euclide demonſtratur, cùm
<
lb
/>
nullius præcedentis alterius propoſitionis
<
lb
/>
auxilio indigeat, erit demonſtranda. </
s
>
<
s
id
="
s.010749
">Inde
<
lb
/>
quinta: nam quòd ad demonſtrationem at
<
lb
/>
tinet, ſola quarta, quam primam vocabi
<
lb
/>
mus, vt quintam ſecundam, indiget: quò
<
lb
/>
verò ad protrahendum lineas, circuli am
<
lb
/>
plitudo nobis propoſita ſufficiet, cùm lineas
<
lb
/>
quantumlibet in directum producere liceat.
<
lb
/>
</
s
>
<
s
id
="
s.010750
">Inde tertia erit nobis, quæ ſeptima & quar
<
lb
/>
ta, qua octaua: nam etſi ab Euclide ex ſe
<
lb
/>
ptima demonſtretur, tamen & ſine abſur
<
lb
/>
do ſic poterit demonſtrari. </
s
>
<
s
id
="
s.010751
">Collocato alte
<
lb
/>
ro trigono ex aduerſo ſuper baſim, lineáque
<
lb
/>
à vertice ad verticem recta ducta: nam con
<
lb
/>
ſtat, vt etiam à Proclo oſtenditur in tertio
<
lb
/>
libro ex ſecunda, & animi communi ſen
<
lb
/>
tentia, trigonos habere angulos ſupremos,
<
lb
/>
& latera illos continentia æqualia, igitur
<
lb
/>
ex prima erunt æquales, transferre autem
<
lb
/>
trigonos licet, cùm Euclides in quarta ſua
<
lb
/>
Propoſitione id admittat. </
s
>
<
s
id
="
s.010752
">Quarta nobis erit
<
lb
/>
nona Euclidis in primo libro: nam de il
<
lb
/>
lo intelligo, donec alterius libri mentio
<
lb
/>
nem adiecero. </
s
>
<
s
id
="
s.010753
">Igitur factis lineis angu
<
lb
/>
lum continentibus æqualibus iuxta circini
<
lb
/>
latitudinem propoſitum, circulos duos ſe
<
lb
/>
cundum datam latitudinem factis centris
<
lb
/>
terminis linearum deſcribam, ſecantes ſe
<
lb
/>
in angulo propoſito & ex aduerſo, ad quam
<
lb
/>
ſectionem è centris circulorum ductis li
<
lb
/>
neis, inde è ſectione ad ſectionem ex ter
<
lb
/>
tia harum, & circuli diffinitione illicò pa
<
lb
/>
tet propoſitum. </
s
>
<
s
id
="
s.010754
">Quòd ſi quis adeò peruer
<
lb
/>
ſus ſit, vt ne admittat circulos alibi ſe
<
lb
/>
ſecare, quàm in angulo, ducta linea in
<
lb
/>
ter fines angulum continentium recta, to
<
lb
/>
ties vtrunque circulos repetemus, donec
<
lb
/>
ſe tandem, aut ſecent, aut contingant. </
s
>
<
s
id
="
s.010755
">Per
<
lb
/>
<
arrow.to.target
n
="
marg1511
"/>
<
lb
/>
ſecundam & primam harum aſſequemur,
<
lb
/>
tandémque per tertiam propoſitum angu
<
lb
/>
lum, ducta ex angulo, ad aduerſam circulo
<
lb
/>
rum ſectionem recta, bifariàm. </
s
>
<
s
id
="
s.010756
">ſecari. </
s
>
<
s
id
="
s.010757
">Quin
<
lb
/>
tam ſtatuemus decimam Euclidis, per præ
<
lb
/>
cedentis modum, vim ac figuram demon
<
lb
/>
ſtratam. </
s
>
</
p
>
<
p
type
="
margin
">
<
s
id
="
s.010758
">
<
margin.target
id
="
marg1510
"/>
<
lb
/>
Primi Eucl.
<
lb
/>
</
s
>
<
s
id
="
s.010759
">noſtræ.
<
lb
/>
</
s
>
<
s
id
="
s.010760
">4 1
<
lb
/>
5 2
<
lb
/>
7 3
<
lb
/>
8 4
<
lb
/>
</
s
>
</
p
>
<
p
type
="
margin
">
<
s
id
="
s.010761
">
<
margin.target
id
="
marg1511
"/>
<
lb
/>
Eucl. </
s
>
<
s
id
="
s.010762
">noſtræ.
<
lb
/>
</
s
>
<
s
id
="
s.010763
">10 6
<
lb
/>
11 7
<
lb
/>
</
s
>
</
p
>
<
p
type
="
main
">
<
s
id
="
s.010764
">Sexta erit vndecima illius: hinc inde ex
<
lb
/>
puncto dato, quantum eſt circuli latitudo
<
lb
/>
capiemus: vtraque verò per quintam diui
<
lb
/>
ſa bifariàm, erunt partes quæ ad punctum
<
lb
/>
iungentur dimidium latitudinis circini, am
<
lb
/>
bæque iunctæ ipſa latitudo, vnde extremis
<
lb
/>
illius lineæ pro centris poſitis, vbi circuli
<
lb
/>
ſe interſecabunt, linea ducta ad punctum
<
lb
/>
datum, ex tertia harum perpendicularis erit.
<
lb
/>
</
s
>
<
s
id
="
s.010765
">Inde decimamtertiam, decimamquartam, &
<
lb
/>
decimamquintam Euclidis, ſeptimam, octa
<
lb
/>
<
arrow.to.target
n
="
marg1512
"/>
<
lb
/>
uam, & nonam harum ſtatuemus, cùm nullis
<
lb
/>
aliis, niſi demonſtratis, iam hîc indigeant. </
s
>
</
p
>
<
p
type
="
margin
">
<
s
id
="
s.010766
">
<
margin.target
id
="
marg1512
"/>
<
lb
/>
13 8
<
lb
/>
14 9
<
lb
/>
15 10
<
lb
/>
Pars tertia.
<
lb
/>
</
s
>
<
s
id
="
s.010767
">11.
<
lb
/>
</
s
>
</
p
>
<
p
type
="
main
">
<
s
id
="
s.010768
">
<
emph
type
="
center
"/>
PARS TERTIÆ DECIMÆ.
<
emph.end
type
="
center
"/>
</
s
>
</
p
>
<
p
type
="
main
">
<
s
id
="
s.010769
">Decima propoſitio erit hæc: Propoſitis
<
lb
/>
duabus lineis inæqualibus ſe tangentibus,
<
lb
/>
de maiore quantum æquale ſit minori abſ
<
lb
/>
cindere: eſtque hæc pars tertiæ Euclidis: at </
s
>
</
p
>
</
chap
>
</
body
>
</
text
>
</
archimedes
>