Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
Text
Text Image
Image
XML
Thumbnail overview
Document information
None
Concordance
Notes
Handwritten
Figures
Content
Thumbnails
page
|<
<
(250)
of 569
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div600
"
type
="
section
"
level
="
1
"
n
="
349
">
<
p
>
<
s
xml:id
="
echoid-s6218
"
xml:space
="
preserve
">
<
pb
o
="
250
"
file
="
0270
"
n
="
270
"
rhead
="
GEOMETRIÆ
"/>
libet portiones extra figuram ad oppoſita latera terminan-
<
lb
/>
tes, & </
s
>
<
s
xml:id
="
echoid-s6219
"
xml:space
="
preserve
">in eadem recta linea conſtitutæ integræ, & </
s
>
<
s
xml:id
="
echoid-s6220
"
xml:space
="
preserve
">inter ſe
<
lb
/>
æquales: </
s
>
<
s
xml:id
="
echoid-s6221
"
xml:space
="
preserve
">Omnia quadrata dicti parallelogrammi ad omnia
<
lb
/>
quadrata inſcriptæ figuræ, cum rectangulis bis ſub eadem
<
lb
/>
figura, & </
s
>
<
s
xml:id
="
echoid-s6222
"
xml:space
="
preserve
">ſub dictarum portionum ijs omnibus, quę extra fi-
<
lb
/>
guram ad vnum dictorum laterum oppoſitorum eiuſdem pa-
<
lb
/>
rallelogrammi terminantur, erunt vt prædictum parallelo-
<
lb
/>
grammum ad inſcriptam figuram.</
s
>
<
s
xml:id
="
echoid-s6223
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s6224
"
xml:space
="
preserve
">Sitigitur parallelogrammum, AN, & </
s
>
<
s
xml:id
="
echoid-s6225
"
xml:space
="
preserve
">illi inſcripta vtcunq; </
s
>
<
s
xml:id
="
echoid-s6226
"
xml:space
="
preserve
">figu-
<
lb
/>
ra, BDMO, & </
s
>
<
s
xml:id
="
echoid-s6227
"
xml:space
="
preserve
">ſumpta pro regula, EN, ſit ducta vtcunque intra
<
lb
/>
parallelogrammum, AN, ipſa, DO, quę cadat etiam tota intra fi-
<
lb
/>
guram, BDMO, ſit etiam ducta alia vtcunque parallela ipſi, EN,
<
lb
/>
nempè, VR, portiones autem eiuſdem, VR, ſint extra figuram,
<
lb
/>
ad latera oppoſita, AE, CN, terminantes .</
s
>
<
s
xml:id
="
echoid-s6228
"
xml:space
="
preserve
">ſ. </
s
>
<
s
xml:id
="
echoid-s6229
"
xml:space
="
preserve
">VI, SR, quæ ſint in-
<
lb
/>
tegræ, & </
s
>
<
s
xml:id
="
echoid-s6230
"
xml:space
="
preserve
">inter ſe æquales. </
s
>
<
s
xml:id
="
echoid-s6231
"
xml:space
="
preserve
">Dico omnia quadrata, AN, ad omnia
<
lb
/>
quadrata figuræ, BDMO, cum rectangulis bis ſub figuræ, BDM
<
lb
/>
O, & </
s
>
<
s
xml:id
="
echoid-s6232
"
xml:space
="
preserve
">ſub trilineis, BCO, ONM, .</
s
>
<
s
xml:id
="
echoid-s6233
"
xml:space
="
preserve
">i. </
s
>
<
s
xml:id
="
echoid-s6234
"
xml:space
="
preserve
">ſub omnibus portionibus, quę
<
lb
/>
terminant ad latus, CN, extra figuram, BDMO, conſtitutis, elie
<
lb
/>
<
figure
xlink:label
="
fig-0270-01
"
xlink:href
="
fig-0270-01a
"
number
="
166
">
<
image
file
="
0270-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0270-01
"/>
</
figure
>
vt, AN, ad figuram, BDMO: </
s
>
<
s
xml:id
="
echoid-s6235
"
xml:space
="
preserve
">Omnia
<
lb
/>
enim quadrata, AN, ad rectangula ſub,
<
lb
/>
A N, & </
s
>
<
s
xml:id
="
echoid-s6236
"
xml:space
="
preserve
">ſub figura, BDMO, ſunt vt, A
<
lb
/>
N, ad figuram, BDMO, ſed rectangula
<
lb
/>
ſub, AN, & </
s
>
<
s
xml:id
="
echoid-s6237
"
xml:space
="
preserve
">ſub figura, BDMO, diui-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0270-01
"
xlink:href
="
note-0270-01a
"
xml:space
="
preserve
">Coroll. 1.
<
lb
/>
26. lib. 2.</
note
>
duntur in rectangula ſub eadem figura, B
<
lb
/>
D MO, & </
s
>
<
s
xml:id
="
echoid-s6238
"
xml:space
="
preserve
">ſub trilineis, BAD, DEM,
<
lb
/>
ſub eadem, & </
s
>
<
s
xml:id
="
echoid-s6239
"
xml:space
="
preserve
">ſub trilineis, BCO, ON
<
lb
/>
M, & </
s
>
<
s
xml:id
="
echoid-s6240
"
xml:space
="
preserve
">in rectangula ſub eadem in eandem
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0270-02
"
xlink:href
="
note-0270-02a
"
xml:space
="
preserve
">A. 23. l. 2.</
note
>
figuram .</
s
>
<
s
xml:id
="
echoid-s6241
"
xml:space
="
preserve
">ſ. </
s
>
<
s
xml:id
="
echoid-s6242
"
xml:space
="
preserve
">in omnia quadrata eiuſdem fi-
<
lb
/>
guræ, BDMO, quia verò linearum æqui-
<
lb
/>
diſtantium, regulæ, EN, portiones, quæ
<
lb
/>
ſunt in eadem recta linea extra figuram adiacentes lateribus oppoſi-
<
lb
/>
tis, AE, CN, ſunt & </
s
>
<
s
xml:id
="
echoid-s6243
"
xml:space
="
preserve
">integræ, & </
s
>
<
s
xml:id
="
echoid-s6244
"
xml:space
="
preserve
">æquales, ideò ſicuti rectangu-
<
lb
/>
lum, VIS, eſt æquale rectangulo, ISR, ita rectangula ſub figura,
<
lb
/>
B DMO, & </
s
>
<
s
xml:id
="
echoid-s6245
"
xml:space
="
preserve
">trilineis, BAD, DEM, erunt æqualia rectangulis
<
lb
/>
ſub eadem figura, BDMO, & </
s
>
<
s
xml:id
="
echoid-s6246
"
xml:space
="
preserve
">ſub trilineis, BCO, ONM, ſunt
<
lb
/>
ergo rectangula ſub, AN, & </
s
>
<
s
xml:id
="
echoid-s6247
"
xml:space
="
preserve
">ſub figura, BDMO, æqualia om-
<
lb
/>
nibus quadratis figuræ, BDMO, cum rectangulis bis ſub eadem,
<
lb
/>
& </
s
>
<
s
xml:id
="
echoid-s6248
"
xml:space
="
preserve
">ſub trilineis, BCO, ONM; </
s
>
<
s
xml:id
="
echoid-s6249
"
xml:space
="
preserve
">omnia autem quadrata, AN, ad
<
lb
/>
rectangula ſub, AN, & </
s
>
<
s
xml:id
="
echoid-s6250
"
xml:space
="
preserve
">ſub figura, BDMO, ſunt vt, AN, ad fi-
<
lb
/>
guram, BDMO; </
s
>
<
s
xml:id
="
echoid-s6251
"
xml:space
="
preserve
">ergo omnia quadrata, AN, ad omnia </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>