Biancani, Giuseppe
,
Aristotelis loca mathematica
,
1615
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 - 355
>
311
312
313
314
315
316
317
318
319
320
<
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 - 355
>
page
|<
<
of 355
>
>|
<
archimedes
>
<
text
>
<
body
>
<
chap
>
<
p
type
="
main
">
<
s
id
="
s.005656
">
<
pb
pagenum
="
34
"
xlink:href
="
009/01/318.jpg
"/>
diſtantiæ linearum. </
s
>
<
s
id
="
s.005657
">ſimile dicendum eſt de ſecunda parte demonſtrationis.</
s
>
</
p
>
<
p
type
="
main
">
<
s
id
="
s.005658
">29 Prima pars probatur ab impoſſibili. </
s
>
<
s
id
="
s.005659
">ſecunda à ſigno, quæ ſuat æqua
<
lb
/>
lia vni tertio &c. </
s
>
<
s
id
="
s.005660
">Idem dicendum de tertia parte.</
s
>
</
p
>
<
p
type
="
main
">
<
s
id
="
s.005661
">30 Probat eſſe parallelas ex 27. primi, quare est
<
expan
abbr
="
eiuſdẽ
">eiuſdem</
expan
>
naturæ cum illa.</
s
>
</
p
>
<
p
type
="
main
">
<
s
id
="
s.005662
">31
<
expan
abbr
="
Eandẽ
">Eandem</
expan
>
habet
<
expan
abbr
="
rationẽ
">rationem</
expan
>
, quam 27. primi. </
s
>
<
s
id
="
s.005663
">per cauſam igitur formalem.</
s
>
</
p
>
<
p
type
="
main
">
<
s
id
="
s.005664
">32 Primò, probat
<
expan
abbr
="
anguiũ
">anguium</
expan
>
externum eſſe æqualem duabus internis, & ap
<
lb
/>
poſitis ex eo, quòd partes anguli externi, ſint æquales partibus illorum: ex
<
lb
/>
æqualitate.ſ partium infert
<
expan
abbr
="
æqualitatẽ
">æqualitatem</
expan
>
totorum: quæ demonſtratio eſt per
<
lb
/>
cauſam materialem. </
s
>
<
s
id
="
s.005665
">Secundò, probat illam adeò celeberrimam, omnis
<
lb
/>
triangulus habet tres, &c. </
s
>
<
s
id
="
s.005666
">quàm fuſiſſimè explicaui ſupra ad tex. 23. primi
<
lb
/>
Poſter. vbi Ariſt. eam in exemplum perfectiſſimæ demonſtrationis adducit.</
s
>
</
p
>
<
p
type
="
main
">
<
s
id
="
s.005667
">33 Partim per 4. primi, partim per 27. primi
<
expan
abbr
="
demõſtrat
">demonſtrat</
expan
>
: quapropter ad
<
lb
/>
earum naturam ſunt referendæ.</
s
>
</
p
>
<
p
type
="
main
">
<
s
id
="
s.005668
">34 Tria probat. </
s
>
<
s
id
="
s.005669
">
<
expan
abbr
="
primũ
">primum</
expan
>
, per 26. primi,
<
expan
abbr
="
ſecundũ
">ſecundum</
expan
>
per illud axioma, ſi æqua
<
lb
/>
libus æqualia adijcias, tota ſunt æqualia, quod duobus angulis applicat.
<
lb
/>
</
s
>
<
s
id
="
s.005670
">quæ demonſtratio eſt à partibus ad tota: à cauſa nimirum materiali. </
s
>
<
s
id
="
s.005671
">ter
<
lb
/>
tium per 4. primi concludit.</
s
>
</
p
>
<
p
type
="
main
">
<
s
id
="
s.005672
">35 Procedit per cauſam materialem: in omni enim caſu probat illa duo
<
lb
/>
parallelogramma eſſe æqualia, quia ſi æqualibus æqualia adijciantur, tota
<
lb
/>
erunt æqualia: vt in præcedenti dictum eſt.</
s
>
</
p
>
<
p
type
="
main
">
<
s
id
="
s.005673
">36 Probat duo eſſe æqualia, quia ſunt vni tertio æqualia: videlicet à ſi
<
lb
/>
gno, à poſteriori.</
s
>
</
p
>
<
p
type
="
main
">
<
s
id
="
s.005674
">37 Probat duo triangula eſſe æqualia, quòd ſint dimidia duorum paral
<
lb
/>
lelogrammorum æqualium: eſt
<
expan
abbr
="
itaq;
">itaque</
expan
>
à cauſa materiali.</
s
>
</
p
>
<
p
type
="
main
">
<
s
id
="
s.005675
">38 Eadem ratione demonſtrat in hac,
<
expan
abbr
="
atq;
">atque</
expan
>
in præcedenti.</
s
>
</
p
>
<
p
type
="
main
">
<
s
id
="
s.005676
">39 Propoſitum probat, ad abſurdum deducendo aduerſarium.</
s
>
</
p
>
<
p
type
="
main
">
<
s
id
="
s.005677
">40 Similiter demonſtrat ac in præcedenti 39.</
s
>
</
p
>
<
p
type
="
main
">
<
s
id
="
s.005678
">41 Probat vnum eſſe duplum alterius, quòd ſit duplum alterius, quod il
<
lb
/>
li æquale eſt. </
s
>
<
s
id
="
s.005679
">videtur à ſigno.</
s
>
</
p
>
<
p
type
="
main
">
<
s
id
="
s.005680
">42 Probat parallelogrammum, &
<
expan
abbr
="
triangulũ
">triangulum</
expan
>
eſſe æqualia, quoniam
<
expan
abbr
="
vtrũ-que
">vtrun
<
lb
/>
que</
expan
>
duplum ſit eiuſdem trianguli: videlicet per cauſam materialem.</
s
>
</
p
>
<
p
type
="
main
">
<
s
id
="
s.005681
">43 Probat duo parallelogramma eſſe ęqualia, quoniam ablatis æquali
<
lb
/>
bus ab æqualibus ſint reſidua. </
s
>
<
s
id
="
s.005682
">cauſa eſt materialis.</
s
>
</
p
>
<
p
type
="
main
">
<
s
id
="
s.005683
">44 Probat parallelogrammum æquari triangulo, quia
<
expan
abbr
="
vtrunq;
">vtrunque</
expan
>
cuidam
<
lb
/>
tertio æquatur. </
s
>
<
s
id
="
s.005684
">à ſigno videlicet.</
s
>
</
p
>
<
p
type
="
main
">
<
s
id
="
s.005685
">45 Probat totum parallelogrammum æquari toti rectilineo; eo, quòd
<
lb
/>
partes amborum totorum ſint æquales: eſt perſpicua cauſa materialis.</
s
>
</
p
>
<
p
type
="
main
">
<
s
id
="
s.005686
">46 Probat quadrilaterum quoddam eſſe quadratum ex definitione qua
<
lb
/>
drati, quia ſ habet quatuor angulos rectos, & quatuor latera æqualia. </
s
>
<
s
id
="
s.005687
">eſt
<
lb
/>
igitur à cauſa formali.</
s
>
</
p
>
<
p
type
="
main
">
<
s
id
="
s.005688
">47 Probat quadratum lateris angulo recto ſubſenſi, eſſe æquale duobus
<
lb
/>
quadratis reliquorum
<
expan
abbr
="
laterũ
">laterum</
expan
>
trianguli illius: & ratio deſumpta eſt à parti
<
lb
/>
bus, quia. </
s
>
<
s
id
="
s.005689
">ſ. </
s
>
<
s
id
="
s.005690
">partes prædicti quadrati æquales ſunt ſingillatim prędictis qua
<
lb
/>
dratis; ergo totum quadratum totis illis quadratis æquale eſt. </
s
>
<
s
id
="
s.005691
">manifeſta eſt
<
lb
/>
cauſa materialis.</
s
>
</
p
>
<
p
type
="
main
">
<
s
id
="
s.005692
">48 Probat angulum quendam eſſe rectum, eo, quòd æqualis ſit cuidam
<
lb
/>
angulo recto. </
s
>
<
s
id
="
s.005693
">eſt à ſigno.</
s
>
</
p
>
</
chap
>
</
body
>
</
text
>
</
archimedes
>