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
|<
<
(88)
of 569
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div213
"
type
="
section
"
level
="
1
"
n
="
138
">
<
p
>
<
s
xml:id
="
echoid-s2180
"
xml:space
="
preserve
">
<
pb
o
="
88
"
file
="
0108
"
n
="
108
"
rhead
="
GEOMETRI Æ
"/>
circulus eum ſecat, producetur ergo ab hoc ſecante plano in ipſis ſo-
<
lb
/>
lidis circulus centrum in axehabens, cuius diameter erit, BD, ha-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0108-01
"
xlink:href
="
note-0108-01a
"
xml:space
="
preserve
">34. huius.</
note
>
bemus igitur duos circulos in eodem plano, circa eandem diametrum,
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0108-02
"
xlink:href
="
note-0108-02a
"
xml:space
="
preserve
">Corol. 34
<
lb
/>
huius.</
note
>
ergo illi erunt congruentes, periphæria autem circuli dicto ſecante
<
lb
/>
plano in dicto ſolido producti eſt in ſuperficie ambiente dictum ſoli-
<
lb
/>
dum, ergo, & </
s
>
<
s
xml:id
="
echoid-s2181
"
xml:space
="
preserve
">periphęria circuli, BNDE, deſcripti, vt dictum eſt,
<
lb
/>
erit in tali ſuperficie, ſcilicet in ſuperficie ſphæræ in figura circuli,
<
lb
/>
ſphæroidis in figura ellipſis, conoidis parabolici in figura parabolæ,
<
lb
/>
& </
s
>
<
s
xml:id
="
echoid-s2182
"
xml:space
="
preserve
">hyperbolici in figura hyperbolę, idem oſtendemus de alijs quibuſ-
<
lb
/>
cumque ſic deſcriptis circulis ab ordinatim applicatis ad dictos axes
<
lb
/>
tanquam à diametris, qui ſint erecti eiſdem ſectionibus, igitur quod
<
lb
/>
proponebatur demonſtratum fuit.</
s
>
<
s
xml:id
="
echoid-s2183
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div215
"
type
="
section
"
level
="
1
"
n
="
139
">
<
head
xml:id
="
echoid-head150
"
xml:space
="
preserve
">THEOREMA XLIV. PROPOS. XLVII.</
head
>
<
p
>
<
s
xml:id
="
echoid-s2184
"
xml:space
="
preserve
">INFRASCRIPTIS poſitis, eadem adhuc ſequi oſten-
<
lb
/>
demus.</
s
>
<
s
xml:id
="
echoid-s2185
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s2186
"
xml:space
="
preserve
">Ijſdem enim expoſitis figuris, præter circulum, ſupponamus ip-
<
lb
/>
fam, AC, non eſſe axem, ſed diametrum, & </
s
>
<
s
xml:id
="
echoid-s2187
"
xml:space
="
preserve
">ad ipſam ordinatim ap-
<
lb
/>
plicari vtcumque, BD, intelligatur autem, BD, diameter cuiuſdam
<
lb
/>
ellipſis ab eadem deſcriptæ, quæ ſit erecta plano propoſitæ figuræ,
<
lb
/>
ſit autem, in figura ellipſis, deſcriptæ ellipſis ſecunda diameter per-
<
lb
/>
pendicularis ipſi, BD, & </
s
>
<
s
xml:id
="
echoid-s2188
"
xml:space
="
preserve
">æqualis ductæ à puncto, B, parallelę tan-
<
lb
/>
<
figure
xlink:label
="
fig-0108-01
"
xlink:href
="
fig-0108-01a
"
number
="
61
">
<
image
file
="
0108-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0108-01
"/>
</
figure
>
genti ellipſim, ABCD, in ex-
<
lb
/>
tremitate eiuſdem axis (quæ
<
lb
/>
tangat in, S,) interiectæ in-
<
lb
/>
ter, BD, & </
s
>
<
s
xml:id
="
echoid-s2189
"
xml:space
="
preserve
">eam, quę ducitur
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0108-03
"
xlink:href
="
note-0108-03a
"
xml:space
="
preserve
">44. huius.</
note
>
à puncto, D, parallela iun-
<
lb
/>
genti puncta, S, A. </
s
>
<
s
xml:id
="
echoid-s2190
"
xml:space
="
preserve
">In figura
<
lb
/>
verò hyperbolæ ſit ſecunda
<
lb
/>
diameter perpendicularis, BD,
<
lb
/>
& </
s
>
<
s
xml:id
="
echoid-s2191
"
xml:space
="
preserve
">æqualis ei, quæ ducitur à
<
lb
/>
puncto, D, parallela tangenti
<
lb
/>
hyperbolam in extremitate a-
<
lb
/>
xis (vt in, S,) interiectæ in-
<
lb
/>
ter, BD, & </
s
>
<
s
xml:id
="
echoid-s2192
"
xml:space
="
preserve
">eam, quę ducitur
<
lb
/>
à puncto, B, parallela iungenti
<
lb
/>
puncta, S, A, & </
s
>
<
s
xml:id
="
echoid-s2193
"
xml:space
="
preserve
">tandem in párabola ſit ſecunda diameter perpendi-
<
lb
/>
cularis quoque ipſi, BD, & </
s
>
<
s
xml:id
="
echoid-s2194
"
xml:space
="
preserve
">æqualis diſtantiæ parallelarum eiuſdem
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0108-04
"
xlink:href
="
note-0108-04a
"
xml:space
="
preserve
">42. huius.</
note
>
axi, quę ducuntur ab extremitatibus ip ſius, B, D. </
s
>
<
s
xml:id
="
echoid-s2195
"
xml:space
="
preserve
">Intelligantur </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>