Biancani, Giuseppe
,
Aristotelis loca mathematica
,
1615
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 - 355
>
Scan
Original
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
<
1 - 30
31 - 60
61 - 90
91 - 120
121 - 150
151 - 180
181 - 210
211 - 240
241 - 270
271 - 300
301 - 330
331 - 355
>
page
|<
<
of 355
>
>|
<
archimedes
>
<
text
>
<
body
>
<
chap
>
<
pb
pagenum
="
206
"
xlink:href
="
009/01/206.jpg
"/>
<
p
type
="
main
">
<
s
id
="
s.003449
">
<
arrow.to.target
n
="
marg272
"/>
</
s
>
</
p
>
<
p
type
="
margin
">
<
s
id
="
s.003450
">
<
margin.target
id
="
marg272
"/>
282</
s
>
</
p
>
<
p
type
="
main
">
<
s
id
="
s.003451
">Sextus locus
<
emph
type
="
italics
"/>
(Rurſus
<
expan
abbr
="
quoq;
">quoque</
expan
>
facilè perſuaderi poteſt ex mota duorurm circulo
<
lb
/>
rum æqualium, nam quiſquis horum moueatur, oportet per maiorem ſemicirculum
<
lb
/>
moueri, & quæcunque alia huiuſmodi constituta ſunt de lineis, fieri non poſſe, vt
<
lb
/>
talis vllus motus peragatur, quin prius omnibus, & ſingulis interiectis occurrat.
<
lb
/>
</
s
>
<
s
id
="
s.003452
">Atque hæc Mathematicorum ſcita, multò magis ab omnibus conceſſa ſunt, quàm
<
lb
/>
illorum dicta.
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
<
p
type
="
main
">
<
s
id
="
s.003453
">Hæc eſt alia ratio, qua probat totam circuli periphæriam eſſe diuiduam.
<
lb
/>
<
figure
id
="
id.009.01.206.1.jpg
"
place
="
text
"
xlink:href
="
009/01/206/1.jpg
"
number
="
128
"/>
<
lb
/>
ſint enim duo circuli æquales primum in eo
<
lb
/>
dem loco,
<
expan
abbr
="
vocenturq́
">vocenturque</
expan
>
; A, & B, deinde circu
<
lb
/>
lus B, moueatur, & diſcedat à circulo A, ma
<
lb
/>
nente; ſtatim
<
expan
abbr
="
namq;
">namque</
expan
>
pars egreſſa E F G, erit
<
lb
/>
maior ſemicirculo, & ſemper fiet maior, ac
<
lb
/>
maior. </
s
>
<
s
id
="
s.003454
">
<
expan
abbr
="
atq;
">atque</
expan
>
in tali motu omnes partes egre
<
lb
/>
dientis circuli ſecantur ab omnibus partibus
<
lb
/>
circuli manentis. </
s
>
<
s
id
="
s.003455
">vnde patet nihil eſſe in eo
<
lb
/>
rum periphærijs, quod non diuidatur. </
s
>
<
s
id
="
s.003456
">nul
<
lb
/>
lum igitur in eis eſt indiuiduum. </
s
>
<
s
id
="
s.003457
">falluntur igitur aduerſarij.</
s
>
</
p
>
<
p
type
="
main
">
<
s
id
="
s.003458
">
<
arrow.to.target
n
="
marg273
"/>
</
s
>
</
p
>
<
p
type
="
margin
">
<
s
id
="
s.003459
">
<
margin.target
id
="
marg273
"/>
283</
s
>
</
p
>
<
p
type
="
main
">
<
s
id
="
s.003460
">Septimus locus
<
emph
type
="
italics
"/>
(Quamuis autem ex confutatis nuper rationibus appareat, ne
<
lb
/>
que probabile, neque neceſſarium eſſe lineas vllas indiuiduas extare, tamen ex ijs
<
lb
/>
etiam, quæ deinceps ſubiungam, multò magis perſpicuum euadet. </
s
>
<
s
id
="
s.003461
">& primò quidem
<
lb
/>
per ea, quæ Mathematici demonſtrant, at que addiſcenda proponunt, quæ mutare
<
lb
/>
non decet, niſt probabiliores rationes habeamus. </
s
>
<
s
id
="
s.003462
">Nam neque lineæ, neque rectæ li
<
lb
/>
neæ definitio cum inſecabili linea conſentit, vt quæ nec inter duo puncta extenſa
<
lb
/>
ſit, nec medium vllam habeat.
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
<
p
type
="
main
">
<
s
id
="
s.003463
">Idem, ſed paulò mutatis verbis poſtea repetit, quæ fortè ab aliquo per
<
lb
/>
errorem addita ſunt. </
s
>
<
s
id
="
s.003464
">Verumenimuerò maximè conſiderandum eſt, quan
<
lb
/>
tum hoc loco Ariſt. Mathematicis demonſtrationibus tribuat: quod dixe
<
lb
/>
rim propter recentiores quoſdam, qui eò audaciæ deuenerunt, vt Euclidis
<
lb
/>
firmiſſimas,
<
expan
abbr
="
atq;
">atque</
expan
>
Ariſtot. teſtimonio,
<
expan
abbr
="
veterumq́
">veterumque</
expan
>
; Philoſophorum omnium
<
lb
/>
comprobatas, negare non verentur Demonſtrationes.</
s
>
</
p
>
<
p
type
="
main
">
<
s
id
="
s.003465
">Cæterùm Ariſt. iterum opinionem
<
expan
abbr
="
aſſerẽtium
">aſſerentium</
expan
>
lineas inſecabiles hoc mo
<
lb
/>
do confutat: nam ſi inquit, lineam illam, quam vocant inſecabilem, eſt non
<
lb
/>
ſolum linea, ſed etiam linea recta, illi conueniret rectæ lineæ definitio, ſed
<
lb
/>
nullo modo poteſt ci conuenire, ergò tollendæ ſunt de rerum natura huiuſ
<
lb
/>
modi lineæ. </
s
>
<
s
id
="
s.003466
">Porrò definitio lineæ eſt, vt ſit longitudo latitudinis expers, &
<
lb
/>
ſi recta ſit ex æquo ſua interiacet puncta extrema, ergò ipſa linea media erit
<
lb
/>
inter duo indiuidua extrema puncta; at verò linea, quam ipſi volunt eſſe
<
lb
/>
indiuiduum quoddam, qua ratione medium erit inter alia duo indiuidua?
<
lb
/>
</
s
>
<
s
id
="
s.003467
">ipſi enim
<
expan
abbr
="
vidẽtur
">videntur</
expan
>
velle iſtam lineam non habere medium vllum, ſi enim con
<
lb
/>
cederent habere medium, iam poſſet in medio ſecari, quod ipſi nequaquam
<
lb
/>
concederent: patet igitur definitionem lineæ minimè illi conuenire, & pro
<
lb
/>
pterea
<
expan
abbr
="
neq;
">neque</
expan
>
eſſe inter lineas enumerandam.</
s
>
</
p
>
<
p
type
="
main
">
<
s
id
="
s.003468
">
<
arrow.to.target
n
="
marg274
"/>
</
s
>
</
p
>
<
p
type
="
margin
">
<
s
id
="
s.003469
">
<
margin.target
id
="
marg274
"/>
284</
s
>
</
p
>
<
p
type
="
main
">
<
s
id
="
s.003470
">Octauus locus
<
emph
type
="
italics
"/>
(Deinde omnes lineæ commenſurabiles erunt: nam omnes ab in
<
lb
/>
diuiduis lineis dimetientur, quæqué; longitudine, quæqué; potentia ſunt commenſurabi
<
lb
/>
les. </
s
>
<
s
id
="
s.003471
">indiuiduæ autem lineæ ſibi ipſis commenſurabiles ſunt longitudine, cum inter ſe
<
lb
/>
fiat æquales; quare potentia quoque, quod ſi hoc eſt, diuiduum erit quadratum.
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
</
chap
>
</
body
>
</
text
>
</
archimedes
>