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
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
<
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
>
<
p
type
="
main
">
<
s
id
="
s.011044
">
<
pb
pagenum
="
599
"
xlink:href
="
016/01/246.jpg
"/>
A D ad latus A B. </
s
>
<
s
id
="
s.011045
">Atque ita etiam ratio
<
lb
/>
ſubtenſæ quatuor lateribus & duobus, &
<
lb
/>
ſubtenſæ ſex lateribus ac tribus, tum alia
<
lb
/>
rum cum latere reſpiciente ſubtenſas. </
s
>
<
s
id
="
s.011046
">Mul
<
lb
/>
tiplex igitur ratio in figuris æquilateris cir
<
lb
/>
culis inſcriptis, & quæ ex his compo
<
lb
/>
nuntur.
<
lb
/>
<
arrow.to.target
n
="
marg1551
"/>
</
s
>
</
p
>
<
p
type
="
margin
">
<
s
id
="
s.011047
">
<
margin.target
id
="
marg1550
"/>
Ratio gene
<
lb
/>
ralis
<
expan
abbr
="
omniũ
">omnium</
expan
>
<
lb
/>
figurarum
<
lb
/>
æqualia ha
<
lb
/>
bentium la
<
lb
/>
tera circulo
<
lb
/>
inſcripta
<
lb
/>
rum.</
s
>
</
p
>
<
p
type
="
margin
">
<
s
id
="
s.011048
">
<
margin.target
id
="
marg1551
"/>
Laterum
<
lb
/>
heptagoni
<
lb
/>
ratio.</
s
>
</
p
>
<
p
type
="
main
">
<
s
id
="
s.011049
">Sed nulla melius, quam heptagoni cir
<
lb
/>
culo inſcripti, & æquilateri. </
s
>
<
s
id
="
s.011050
">Si igitur he
<
lb
/>
ptagonus deſcriptus ABCDEFG, & duo
<
lb
/>
bus lateribus ſubtenſa AF & B F ſubtenſa
<
lb
/>
A B, & AF, cumque vt demonſtratum eſt,
<
lb
/>
angulus F B A duplus ſit angulo A F B, &
<
lb
/>
arcus BCDEF duplus eiſdem rationibus ar
<
lb
/>
cui AGF, erit angulus BAF duplus angulo
<
lb
/>
ABF, quare ex demonſtrata proportione
<
lb
/>
BA, & BF ad AF vt AF ad AB: itémque per
<
lb
/>
<
expan
abbr
="
eandẽ
">eandem</
expan
>
AB & AF, ad BF vt BF ad AF. </
s
>
<
s
id
="
s.011051
">Refle
<
lb
/>
xa igitur hæc bis proportio vocabitur. </
s
>
<
s
id
="
s.011052
">Po
<
lb
/>
namus igitur A B nouem, poſita igitur AF
<
lb
/>
ſexdecim & BF viginti, ſi propoſitio viginti
<
lb
/>
nouem ad ſexdecim eſſet qualis ſexdecim ad
<
lb
/>
<
expan
abbr
="
nouẽ
">nouem</
expan
>
haberemus latera trigoni ABF. </
s
>
<
s
id
="
s.011053
">Sed
<
expan
abbr
="
cũ
">cum</
expan
>
<
lb
/>
maior ſit proportio vigintinouem ad ſexde
<
lb
/>
cim, quàm ſexdecim ad nouem, ponemus
<
lb
/>
AF ſexdecim, ac rem habebis prope A B
<
lb
/>
200. A F 359. BF 448. vel per Alizam
<
lb
/>
regulam poſita AF. 1. erit BF. </
s
>
<
s
id
="
s.011054
">R Mut. </
s
>
<
s
id
="
s.011055
">7/54 in
<
lb
/>
2 1/3 ( m 1/3. ex prima æſtimatione. </
s
>
<
s
id
="
s.011056
">Quibus
<
lb
/>
habitis, ſi ducatur ex B linea per centrum,
<
lb
/>
& vbi cadit in circuli periferia linea ad F
<
lb
/>
<
figure
id
="
id.016.01.246.1.jpg
"
xlink:href
="
016/01/246/1.jpg
"
number
="
104
"/>
<
lb
/>
& ad A, habebis quadrilaterum cum duo
<
lb
/>
bus dimetientibus, cuius duo latera, & di
<
lb
/>
metientium vna erit cognita. </
s
>
<
s
id
="
s.011057
">Duos inſu
<
lb
/>
per trigonos orthogonios, quorum baſis
<
lb
/>
erit diameter circuli: vnde poſita reliqua
<
lb
/>
dimetientium re, cùm dimetientibus re
<
lb
/>
ctangulum æquale ſit rectangulis duobus
<
lb
/>
quæ fiunt ex lateribus quadranguli inuicem
<
lb
/>
oppoſitis per demonſtrata à Ptolomæo, erit
<
lb
/>
ex his, quæ docuimus in Arte magna,
<
lb
/>
compoſitis minoribus capitulis ratio dia
<
arrow.to.target
n
="
marg1552
"/>
<
lb
/>
metri circuli ad A B latus heptagoni co
<
lb
/>
gnita. </
s
>
<
s
id
="
s.011058
">Ex his igitur conſtat methodi reſo
<
lb
/>
lutoriæ, cuius toties Galenus meminit, ex
<
lb
/>
quiſitiſſimum, cui non par eſt in medica
<
lb
/>
arte exemplum. </
s
>
<
s
id
="
s.011059
">Propoſitum in circulo co
<
lb
/>
gnitæ diametri heptagonum deſcribere: fa
<
lb
/>
ctum iam ſupponamus, & ſit ſuprà deſ
<
lb
/>
criptus: oportet igitur ſcire, qualiter de
<
lb
/>
ducta diametro deducenda ſit AB. </
s
>
<
s
id
="
s.011060
">Vt ve
<
lb
/>
rò hoc ſciamus, ratio A B ad diametrum
<
lb
/>
excogitanda eſt: vt verò hæc habeatur, ra
<
lb
/>
tio ad A F, & F B quærenda erit: vt
<
lb
/>
hanc habeas, excogitata eſt rurſus angu
<
lb
/>
lorum proportio, quæ ſola eſt manifeſta.
<
lb
/>
</
s
>
<
s
id
="
s.011061
">Inde ea habita quærendum, quòd hæc
<
lb
/>
proportio inter latera decernat. </
s
>
<
s
id
="
s.011062
">Atque hæc
<
lb
/>
bis reflexa proportio dicitur. </
s
>
<
s
id
="
s.011063
">Hanc cùm
<
lb
/>
ex reflexis ſimplicibus conſtet, diuiſam
<
lb
/>
demonſtrare oportet. </
s
>
<
s
id
="
s.011064
">Atque hic eſt finis
<
lb
/>
reſolutoriæ methodi. </
s
>
<
s
id
="
s.011065
">Ab hoc igitur fine,
<
lb
/>
compoſita methodus, quam præpoſuimus
<
lb
/>
in laterum heptagoni demonſtratione, ini
<
lb
/>
tium ſumit. </
s
>
<
s
id
="
s.011066
">Sed & in his quandoque error
<
lb
/>
contingit, ſi quis non diligenter omninò
<
lb
/>
aduertat. </
s
>
<
s
id
="
s.011067
">Cuius rei exemplum eſt: ſit cir
<
lb
/>
culus A B C, in eo diameter B C, cui
<
lb
/>
<
figure
id
="
id.016.01.246.2.jpg
"
xlink:href
="
016/01/246/2.jpg
"
number
="
105
"/>
<
lb
/>
ſupereſt ad perpendiculum D A: ex A in
<
lb
/>
quam videtur deduci poſſe linea aliqua ſe
<
lb
/>
cans BC, vt A E F, ita vt ſit CE ad EA,
<
lb
/>
vt AE ad EF, quia CB poteſt quantumuis
<
lb
/>
augeri, quod tamen fieri non poteſt: etſi
<
lb
/>
fieri poſſet, Aliza regula non indiguiſſe
<
lb
/>
mus: quia poſita BC, 10. AE puta 6. fieret
<
lb
/>
<
expan
abbr
="
cõfeſtim
">confeſtim</
expan
>
ED cognita, ideoque & EC & EB,
<
lb
/>
& quia proportio C E ad E A, eſt velut
<
lb
/>
EF ad EB, ex demonſtratis ab Euclide in
<
lb
/>
3. Elementorum, fieret, vt aggregato pri
<
lb
/>
mæ, & quartæ quantitatis, tum tertia co
<
lb
/>
gnitis, vt quantitates cognoſcerentur. </
s
>
<
s
id
="
s.011068
">Igi
<
lb
/>
tur cubi, & alicuius numeri æqualis, de
<
lb
/>
cem rebus notum eſt capitulum. </
s
>
<
s
id
="
s.011069
">Diſſolu
<
lb
/>
tio paralogiſmi eſt, quia iam AD eſt me
<
lb
/>
dia inter partes C D & BD, vt notum eſt
<
lb
/>
per ſe, & ſemper creſcit proportio A E ad
<
lb
/>
EF, magis quam CE ad E A, igitur pro
<
lb
/>
portio CE ad E A minor eſt proportione
<
lb
/>
AE ad EF. </
s
>
<
s
id
="
s.011070
">Vbicunque tamen punctus aſ
<
lb
/>
ſumatur in circunferentia A B ſemper de
<
lb
/>
duci poterit, quia proportio partis CB ter
<
lb
/>
minatæ ad deductam ex puncto illo ad per
<
lb
/>
pendiculum eſt maior, quam deductæ ad
<
lb
/>
ad perpendiculum AD reſiduum, cui ſem
<
lb
/>
per eſt æquale, & prior proportio minùs
<
lb
/>
augetur quam poſterior, igitur quandoque
<
lb
/>
peruenient ad æqualitatem. </
s
>
<
s
id
="
s.011071
">In vniuerſum
<
lb
/>
igitur paralogiſmi fiunt, vel cum aſſumitur
<
lb
/>
aliquid in
<
expan
abbr
="
cõſtructione
">conſtructione</
expan
>
problematis, quo
<
expan
abbr
="
nõ
">non</
expan
>
<
lb
/>
vtimur in demonſtratione, vel cum vtimur
<
lb
/>
principio non vero, ſed veriſimili, vel cum
<
lb
/>
aſſumimus non demonſtrata pro demonſtra
<
lb
/>
tis, vel pro medio, quod medium non eſt.
<
lb
/>
</
s
>
<
s
id
="
s.011072
">Omnia autem hæc magis contingunt in
<
lb
/>
<
figure
id
="
id.016.01.246.3.jpg
"
xlink:href
="
016/01/246/3.jpg
"
number
="
106
"/>
<
lb
/>
remotis à ſenſu, vt corporibus, & diuerſi </
s
>
</
p
>
</
chap
>
</
body
>
</
text
>
</
archimedes
>