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
|<
<
(86)
of 569
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div209
"
type
="
section
"
level
="
1
"
n
="
135
">
<
p
>
<
s
xml:id
="
echoid-s2126
"
xml:space
="
preserve
">
<
pb
o
="
86
"
file
="
0106
"
n
="
106
"
rhead
="
GEOMETRIE
"/>
dem ſecantis figuram, & </
s
>
<
s
xml:id
="
echoid-s2127
"
xml:space
="
preserve
">alterius acti per axem recto ad pla-
<
lb
/>
num ſecans. </
s
>
<
s
xml:id
="
echoid-s2128
"
xml:space
="
preserve
">Archim. </
s
>
<
s
xml:id
="
echoid-s2129
"
xml:space
="
preserve
">ibid. </
s
>
<
s
xml:id
="
echoid-s2130
"
xml:space
="
preserve
">Propoſ. </
s
>
<
s
xml:id
="
echoid-s2131
"
xml:space
="
preserve
">14.</
s
>
<
s
xml:id
="
echoid-s2132
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div210
"
type
="
section
"
level
="
1
"
n
="
136
">
<
head
xml:id
="
echoid-head147
"
xml:space
="
preserve
">THEOREMA XLI. PROPOS. XLIV.</
head
>
<
p
>
<
s
xml:id
="
echoid-s2133
"
xml:space
="
preserve
">SI ſphæroides plano ſecetur non recto ad axem, ſectio erit
<
lb
/>
ellipſis, diameter verò ipſius maior erit concepta in ſphę-
<
lb
/>
roide ſectio duorum planorum, eius ſcilicet, quod ſecat figu-
<
lb
/>
ram, & </
s
>
<
s
xml:id
="
echoid-s2134
"
xml:space
="
preserve
">eius, quod ducitur per axem recto ad planum ſecans.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s2135
"
xml:space
="
preserve
">Arch. </
s
>
<
s
xml:id
="
echoid-s2136
"
xml:space
="
preserve
">ibid. </
s
>
<
s
xml:id
="
echoid-s2137
"
xml:space
="
preserve
">Propoſ. </
s
>
<
s
xml:id
="
echoid-s2138
"
xml:space
="
preserve
">15.</
s
>
<
s
xml:id
="
echoid-s2139
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s2140
"
xml:space
="
preserve
">Minor verò diameter ſic habetur. </
s
>
<
s
xml:id
="
echoid-s2141
"
xml:space
="
preserve
">Sit Sphæroides, vel conoides
<
lb
/>
hyperbolicum, BDMF, axis, BM, centrum, A, ellipſis verò per
<
lb
/>
<
figure
xlink:label
="
fig-0106-01
"
xlink:href
="
fig-0106-01a
"
number
="
59
">
<
image
file
="
0106-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0106-01
"/>
</
figure
>
axem tranſiens in
<
lb
/>
ſphæroide, BDM
<
lb
/>
F, in conoide verò
<
lb
/>
hyperbola, NCO.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s2142
"
xml:space
="
preserve
">Secetur autem ſphę-
<
lb
/>
roides, vel conoides
<
lb
/>
plano non recto ad
<
lb
/>
axem, ſed erecto fi-
<
lb
/>
guræ, BDMF, ex
<
lb
/>
quo fiat in ipſis ſe-
<
lb
/>
ctio, DF, hæc erit
<
lb
/>
ellipſis, cuius maior
<
lb
/>
diameter, DF. </
s
>
<
s
xml:id
="
echoid-s2143
"
xml:space
="
preserve
">In-
<
lb
/>
ueniatur nunc ver-
<
lb
/>
tex ellipſis, ſeu hy-
<
lb
/>
perbolæ, BDMF,
<
lb
/>
reſpectu ipſius, DF, qui ſit, C, & </
s
>
<
s
xml:id
="
echoid-s2144
"
xml:space
="
preserve
">iungatur, CB, ac per, B, aga-
<
lb
/>
tur, BG, tangens in, B, ipſam ellipſim, ſeu hyperbolam, tandem à
<
lb
/>
puncto, D, parallela ipſi, BG, & </
s
>
<
s
xml:id
="
echoid-s2145
"
xml:space
="
preserve
">à puncto, F, parallela ipſi, CB,
<
lb
/>
produc antur, DE, FE, quæ inuicem concurrent vt in, E. </
s
>
<
s
xml:id
="
echoid-s2146
"
xml:space
="
preserve
">Dico
<
lb
/>
igitur, quod erit, ED, minor diameter eiuſdem ellipſis, DF.</
s
>
<
s
xml:id
="
echoid-s2147
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s2148
"
xml:space
="
preserve
">Hoc autem demonſtrat ibid. </
s
>
<
s
xml:id
="
echoid-s2149
"
xml:space
="
preserve
">Dauid Riualtus in Commentarijs in
<
lb
/>
Archim. </
s
>
<
s
xml:id
="
echoid-s2150
"
xml:space
="
preserve
">ad Propoſ. </
s
>
<
s
xml:id
="
echoid-s2151
"
xml:space
="
preserve
">14. </
s
>
<
s
xml:id
="
echoid-s2152
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s2153
"
xml:space
="
preserve
">15.</
s
>
<
s
xml:id
="
echoid-s2154
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
</
text
>
</
echo
>