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
Table of handwritten notes
<
1 - 8
[out of range]
>
<
1 - 8
[out of range]
>
page
|<
<
(317)
of 569
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div757
"
type
="
section
"
level
="
1
"
n
="
446
">
<
pb
o
="
317
"
file
="
0337
"
n
="
337
"
rhead
="
LIBER IV.
"/>
</
div
>
<
div
xml:id
="
echoid-div758
"
type
="
section
"
level
="
1
"
n
="
447
">
<
head
xml:id
="
echoid-head467
"
xml:space
="
preserve
">THEOREMA XXIV. PROPOS. XXVI.</
head
>
<
p
>
<
s
xml:id
="
echoid-s7635
"
xml:space
="
preserve
">INeadem antecedentis figura oſtendemus omnia quadra-
<
lb
/>
ta portionis, BSF, ad rectangula ſub eadem portione,
<
lb
/>
BSF, & </
s
>
<
s
xml:id
="
echoid-s7636
"
xml:space
="
preserve
">ſub figura, SEF, regula communi, BF, eſſe vt, B
<
lb
/>
F, ad, FE.</
s
>
<
s
xml:id
="
echoid-s7637
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s7638
"
xml:space
="
preserve
">Eſt enim quadratum, BF, ad rectangulum ſub, BF, FE, vt, B
<
lb
/>
F, ad, FE; </
s
>
<
s
xml:id
="
echoid-s7639
"
xml:space
="
preserve
">ſimiliter ducta vtcunque, CD, parallela regulę, BF,
<
lb
/>
oſtendemus quadratum, CD, ad rectangulum, ſub, CD, DZ,
<
lb
/>
eſſe vt, CD, ad, DZ, eſt autem vt, BF, ad, FE, ita, CD, ad,
<
lb
/>
DZ, ergo quadratum, BF, ad rectangulum, BFE, erit vt qua-
<
lb
/>
dratum, CD, ad rectangulum, CDZ, ſic oſtendemus quamlibet
<
lb
/>
ductam intra portionem, BSF, parallelam regulę, BF, ad eiuſdem
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0337-01
"
xlink:href
="
note-0337-01a
"
xml:space
="
preserve
">Corol.
<
lb
/>
4. 1. 2.</
note
>
portionem incluſam figura, SFE, eſſe vt quadratum, BF, ad re-
<
lb
/>
ctangulum ſub, BF, FE, ergo quadratum, BF, ad rectangulum
<
lb
/>
ſub, BF, FE, erit vt omnia quadrata portionis, BSF, ad rectan-
<
lb
/>
gula ſub portione, BSF, & </
s
>
<
s
xml:id
="
echoid-s7640
"
xml:space
="
preserve
">ſub figura, SEF, vt autem quadratum,
<
lb
/>
BF, ad rectangulum ſub, BF, FE, ita, BF, ad, FE, ergo omnia
<
lb
/>
quadrata portionis, BSF, ad rectangula ſub portione, BSF, & </
s
>
<
s
xml:id
="
echoid-s7641
"
xml:space
="
preserve
">fi-
<
lb
/>
gura, ESF, erunt vt, BF, ad, FE, quod oſtendere opus erat.</
s
>
<
s
xml:id
="
echoid-s7642
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div760
"
type
="
section
"
level
="
1
"
n
="
448
">
<
head
xml:id
="
echoid-head468
"
xml:space
="
preserve
">THEOREMA XXV. PROPOS. XXVII.</
head
>
<
p
>
<
s
xml:id
="
echoid-s7643
"
xml:space
="
preserve
">SI intra curuam parabolæ duæ vtcunque ducantur rectæ
<
lb
/>
lineę in eandem @terminatæ, quarum vna rectè, altera
<
lb
/>
obliquè axim ſecet, ſint autem conſtitutarum ab eiſdem pa-
<
lb
/>
rabolarum diametri inter ſe æquales: </
s
>
<
s
xml:id
="
echoid-s7644
"
xml:space
="
preserve
">Omnia quadrata pa-
<
lb
/>
rabolæ per eam, quæ rectè axim ſecat, conſtitutæ, regula
<
lb
/>
eadem, erunt æqualia rectangulis ſub parabola per obli-
<
lb
/>
quam ad axem conſtituta, regula eadem, & </
s
>
<
s
xml:id
="
echoid-s7645
"
xml:space
="
preserve
">ſub figura di-
<
lb
/>
ſtantiarum eiuſdem parabolæ per obliquam ad axem con-
<
lb
/>
ſtitutæ.</
s
>
<
s
xml:id
="
echoid-s7646
"
xml:space
="
preserve
"/>
</
p
>
<
figure
number
="
227
">
<
image
file
="
0337-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0337-01
"/>
</
figure
>
</
div
>
</
text
>
</
echo
>