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
>
71
72
73
74
75
76
77
78
79
80
<
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.001215
">
<
pb
pagenum
="
65
"
xlink:href
="
009/01/065.jpg
"/>
quod tamen non obſtat, quominus probare poſſit, aliquando poſſe
<
expan
abbr
="
cõſtrni
">conſtrui</
expan
>
,
<
lb
/>
& eſſe aliquod particulare triangulum, vt fit in prædicta demonſtratione,
<
lb
/>
Euclidis.</
s
>
</
p
>
<
p
type
="
main
">
<
s
id
="
s.001216
">
<
arrow.to.target
n
="
marg71
"/>
</
s
>
</
p
>
<
p
type
="
margin
">
<
s
id
="
s.001217
">
<
margin.target
id
="
marg71
"/>
71</
s
>
</
p
>
<
p
type
="
main
">
<
s
id
="
s.001218
">Tex. 11.
<
emph
type
="
italics
"/>
(Manifeſtum autem, & ſic, propter quid eſt rectus in ſemicirculo)
<
emph.end
type
="
italics
"/>
<
lb
/>
affert exemplum demonſtrationis per cauſam materialem,
<
expan
abbr
="
idq́
">idque</
expan
>
; vti ſolet ex
<
lb
/>
Mathematicis petitum, eſt enim apud Euclidem 31. demonſtratio 3. Elem.
<
lb
/>
vbi ipſe oſtendit angulum in ſemicirculo eſſe rectum. </
s
>
<
s
id
="
s.001219
">Vbi aduertendum eſt
<
lb
/>
propoſitionem hanc 31. ab Euclide demonſtrari duobus modis; ex quibus
<
lb
/>
ſecundum innuit hoc loco Ariſt. cui aſcripta eſt figura ſimilis huic noſtræ;
<
lb
/>
in editione Clauiana. </
s
>
<
s
id
="
s.001220
">quod fortè non benè aduertens Iacobus Zabarella,
<
lb
/>
alioquin in his ſatis oculatus incidit in errorem, dicens, ſe nullo pacto vi
<
lb
/>
dere medium Euclidianæ demonſtrationis eſſe cauſam materialem; quod
<
lb
/>
tamen nos mox aperiemus. </
s
>
<
s
id
="
s.001221
">per angulum in ſemicirculo intelligas eum, qui
<
lb
/>
fit à lineis ductis ab extremitatibus diametri, & ſimul in quoduis punctum
<
lb
/>
<
figure
id
="
id.009.01.065.1.jpg
"
place
="
text
"
xlink:href
="
009/01/065/1.jpg
"
number
="
32
"/>
<
lb
/>
circumferentiæ coeuntibus, vt in figura
<
lb
/>
præſenti vides lineas A C, B C, ad C, pun
<
lb
/>
ctum conuenire,
<
expan
abbr
="
ibiq́
">ibique</
expan
>
; facere angulum,
<
lb
/>
A C B, qui dicitur angulus in ſemicircu
<
lb
/>
lo, quia deſcriptus eſt in ſemicirculo A
<
lb
/>
C B.
<
expan
abbr
="
eſtq́
">eſtque</
expan
>
; ſanè mirabilis hæc ſemicirculi
<
lb
/>
proprietas, cum
<
expan
abbr
="
vbicunq;
">vbicunque</
expan
>
punctum C, in
<
lb
/>
periphæria ſumptum fuerit, ſemper ta
<
lb
/>
men angulus A C B, fiat rectus. </
s
>
<
s
id
="
s.001222
">quod Euclides eodem prorſus medio, quod
<
lb
/>
Ariſt. hic innuit, hoc modo demonſtrat. </
s
>
<
s
id
="
s.001223
">ducta enim recta D C, à centro D,
<
lb
/>
ad punctum C, exurgunt duo lſoſcelia triangula A D C, C D B, ergo per
<
lb
/>
5. primi, anguli D C A, D A C, ſunt æquales: pariter anguli D C B, D B C,
<
lb
/>
æquales ſunt. </
s
>
<
s
id
="
s.001224
">& quia per 32. primi, anguli D A C, D C A, ſimul ſunt æqua
<
lb
/>
les angulo externo C D B, & inter ſe æquales, erit angulus A C D, dimidium
<
lb
/>
anguli C D B. eadem ratione probatur angulus D C B, eſſe dimidium an
<
lb
/>
guli C D A. ergo totus angulus A C B, dimidium erit duorum angulorum
<
lb
/>
A D C, C D B, qui per 13. primi, ſunt vel recti, vel duobus rectis
<
expan
abbr
="
æquiualẽt
">æquiualent</
expan
>
.
<
lb
/>
</
s
>
<
s
id
="
s.001225
">Sequitur igitur, angulum A C B, in ſemicirculo eſſe dimidium duorum re
<
lb
/>
ctorum; & quia omnes recti ſunt æquales, ſequitur dimidium duorum re
<
lb
/>
ctorum, nihil aliud eſſe, quam vnum rectum angulum, ergo angulus in ſe
<
lb
/>
micirculo, cum ſit ſemiſſis duorum
<
expan
abbr
="
rectorũ
">rectorum</
expan
>
, erit vnus rectus angules; quod
<
lb
/>
erat probandum. </
s
>
<
s
id
="
s.001226
">ex quibus vides medium illud, quod Ariſt. aſſumpſit, eſſe
<
lb
/>
omnino idem cum eo, quo Euclides vtitur, ſcilicet, eſſe dimidium duorum
<
lb
/>
rectorum, & propterea eſſe rectum: quod etiam medium in toto demon
<
lb
/>
ſtrationis decurſu eſt vltimum, & principale, quod proximè concluſionem
<
lb
/>
attingit, & propterea dici meretur eſſe medium huius demonſtrationis.
<
lb
/>
</
s
>
<
s
id
="
s.001227
">Cæterum, quod medium iſtud ſit in genere cauſæ materialis, patet ex eo,
<
lb
/>
quod eſt, eſſe dimidium; nam eſſe dimidium, vel eſſe tertiam partem, & ſi
<
lb
/>
milia, nihil aliud eſt, quam eſſe partem; eſſe autem partem eſt eſſe materiam
<
lb
/>
totius, etiam ex ſententia ipſius Ariſt. ex hac præterea materia conflatur
<
lb
/>
definitio minoris extremi, vel ſubiecti; dum dicitur, angulus in ſemicircu
<
lb
/>
lo eſt dimidium duorum rectorum. </
s
>
<
s
id
="
s.001228
">ſyllogiſmus enim reducitur tandem ad </
s
>
</
p
>
</
chap
>
</
body
>
</
text
>
</
archimedes
>