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
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
<
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
="
207
"
xlink:href
="
009/01/207.jpg
"/>
<
p
type
="
main
">
<
s
id
="
s.003472
">Pergit adhuc nouis rationibus aduerſarios refellere, dicens, ſi extarent
<
lb
/>
huiuſmodi indiuiduæ lineæ, ſequeretur omnes omninò lineas eſſe commen
<
lb
/>
ſurabiles, quod eſt contra demonſtrata in 10. Elem. quia cum omnes lineæ
<
lb
/>
<
expan
abbr
="
conſtẽt
">conſtent</
expan
>
per ipſos ex lineis atomis, iſtæ atomæ eſſent omnium linearum com
<
lb
/>
munes menſuræ, vnde & illæ, quæ dicuntur potentia tantum commenſura
<
lb
/>
biles, vt ſupra explicaui, erunt etiam commenſurabiles longitudine. </
s
>
<
s
id
="
s.003473
">indiui
<
lb
/>
duæ verò ipſæ, cum ſint inuicem æquales, erunt ipſæ
<
expan
abbr
="
quoq;
">quoque</
expan
>
commenſurabi
<
lb
/>
les longitudine, quare & potentia, omnes enim longitudine commenſura
<
lb
/>
biles, ſunt etiam potentia commenſurabiles, ex 9. 10. vnde ſequitur qua
<
lb
/>
drata earum omnia eſſe
<
expan
abbr
="
quoq;
">quoque</
expan
>
commenſurabilia:
<
expan
abbr
="
atq;
">atque</
expan
>
hinc conſequitur, in
<
lb
/>
quit, ea eſſe
<
expan
abbr
="
quoq;
">quoque</
expan
>
diuidua (quam conſecutionem probat infra num. </
s
>
<
s
id
="
s.003474
">290.)
<
lb
/>
vnde ſequeretur ipſam
<
expan
abbr
="
quoq;
">quoque</
expan
>
lineam latus quadrati poſſe diuidi, non igitur
<
lb
/>
ponenda erat indiuidua.</
s
>
</
p
>
<
p
type
="
main
">
<
s
id
="
s.003475
">
<
arrow.to.target
n
="
marg275
"/>
</
s
>
</
p
>
<
p
type
="
margin
">
<
s
id
="
s.003476
">
<
margin.target
id
="
marg275
"/>
285</
s
>
</
p
>
<
p
type
="
main
">
<
s
id
="
s.003477
">Nonus Iocus, cuius latinam interpretationem, cum admodum eſſet de
<
lb
/>
prauata ex græco textu, in hunc modum correxi
<
emph
type
="
italics
"/>
(Præterea cùm circa maio
<
lb
/>
rem latitudinem facit applicata, æquale ei, quod ab indiuidua, & pedali copulatis
<
lb
/>
circa bipedalem, minorem faciet latitudinem, quàm ſit indiuidua: erit minus, quod
<
lb
/>
circa indiuiduam)
<
emph.end
type
="
italics
"/>
ideſt cùm minor linea applicata cum maiore, latitudinem
<
lb
/>
<
figure
id
="
id.009.01.207.1.jpg
"
place
="
text
"
xlink:href
="
009/01/207/1.jpg
"
number
="
129
"/>
<
lb
/>
faciat. </
s
>
<
s
id
="
s.003478
">v. g. linea minor A B, applicata cum ma
<
lb
/>
iori B C, vt in figura, ita vt contineant figuram
<
lb
/>
A B C D. </
s
>
<
s
id
="
s.003479
">Minor A B, facit latitudinem figuræ,
<
lb
/>
maior verò B C, facit longitudinem. </
s
>
<
s
id
="
s.003480
">Iam cum
<
lb
/>
aduerſarij velint extare huiuſmodi lineas ato
<
lb
/>
mas, conſtituatur figura ſub vna ex illis, quæ ſit v. g. A B, & altera maiori,
<
lb
/>
quæ ſit pedalis, v. g. B C, vt in præcedenti figura, ſumatur deinde linea bi
<
lb
/>
<
figure
id
="
id.009.01.207.2.jpg
"
place
="
text
"
xlink:href
="
009/01/207/2.jpg
"
number
="
130
"/>
<
lb
/>
pedalis E F, cui per 45. primi ap
<
lb
/>
plicetur ſpatium E F G H, æquale
<
lb
/>
ſpatio ſuperiori A B C D, neceſſa
<
lb
/>
riò latitudo E H, huius ſecundæ fi
<
lb
/>
guræ minor erit quàm latitudo il
<
lb
/>
lius, hoc eſt minor, quàm ſit indiuidua A B, quod eſt abſurdum. </
s
>
<
s
id
="
s.003481
">vel dicere
<
lb
/>
oportet
<
expan
abbr
="
ſpatiũ
">ſpatium</
expan
>
circa indiuiduam A B, eſſe minus quàm iſtud poſterius, quod
<
lb
/>
eſt contra conſtructionem, & propterea pariter inconueniens, non igitur
<
lb
/>
huiuſmodi lineæ ſunt ponendæ.</
s
>
</
p
>
<
p
type
="
main
">
<
s
id
="
s.003482
">
<
arrow.to.target
n
="
marg276
"/>
</
s
>
</
p
>
<
p
type
="
margin
">
<
s
id
="
s.003483
">
<
margin.target
id
="
marg276
"/>
286</
s
>
</
p
>
<
p
type
="
main
">
<
s
id
="
s.003484
">Decimus locus
<
emph
type
="
italics
"/>
(Cum ex tribus datis lineis triangulus componatur, ex tribus
<
lb
/>
<
expan
abbr
="
quoq;
">quoque</
expan
>
indiuiduis lineis componi poterit. </
s
>
<
s
id
="
s.003485
">in omni autem æquilatero perpendicularis
<
lb
/>
in mediam baſim incidit, quare, & in medium indiuiduæ.
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
<
p
type
="
main
">
<
s
id
="
s.003486
">Ex 22. primi Elem. ex tribus datis lineis, quarum quælibet duæ ſint, re
<
lb
/>
liqua maiores poteſt conſtitui triangulum: poterit igitur ex tribus indiui
<
lb
/>
<
figure
id
="
id.009.01.207.3.jpg
"
place
="
text
"
xlink:href
="
009/01/207/3.jpg
"
number
="
131
"/>
<
lb
/>
duis conſtitui
<
expan
abbr
="
triãgulum
">triangulum</
expan
>
,
<
expan
abbr
="
illudq́
">illudque</
expan
>
; æquilaterum, cum omnes in
<
lb
/>
diuiduæ lineæ ſint æquales. </
s
>
<
s
id
="
s.003487
">ſit igitur ex eis triangulum A B C,
<
lb
/>
ſi igitur ab angulo A, ducatur perpendicularis A D, ad baſim
<
lb
/>
B C, eam bifariam ſecabit ex ſcholio 26. primi, erit igitur li
<
lb
/>
nea B C, ſecabilis, contra quam aduerſarij opinantur.</
s
>
</
p
>
<
p
type
="
main
">
<
s
id
="
s.003488
">
<
arrow.to.target
n
="
marg277
"/>
</
s
>
</
p
>
<
p
type
="
margin
">
<
s
id
="
s.003489
">
<
margin.target
id
="
marg277
"/>
287</
s
>
</
p
>
<
p
type
="
main
">
<
s
id
="
s.003490
">Vndecimus locus
<
emph
type
="
italics
"/>
(Si quadratum ex quatuor indiuiduis conſtituatur diametro
<
lb
/>
protracta, & perpendiculari ducta, quadrati coſta potentia
<
expan
abbr
="
perpẽdicularem
">perpendicularem</
expan
>
, diame-
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
</
chap
>
</
body
>
</
text
>
</
archimedes
>