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
|<
<
(362)
of 569
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div881
"
type
="
section
"
level
="
1
"
n
="
528
">
<
p
>
<
s
xml:id
="
echoid-s9152
"
xml:space
="
preserve
">
<
pb
o
="
362
"
file
="
0382
"
n
="
382
"
rhead
="
GEOMETRIÆ
"/>
regulam, ZG, vt in poſteriore dicti Theor. </
s
>
<
s
xml:id
="
echoid-s9153
"
xml:space
="
preserve
">parte dictum eſt.</
s
>
<
s
xml:id
="
echoid-s9154
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div883
"
type
="
section
"
level
="
1
"
n
="
529
">
<
head
xml:id
="
echoid-head549
"
xml:space
="
preserve
">COROLLARIVM XXV.</
head
>
<
p
>
<
s
xml:id
="
echoid-s9155
"
xml:space
="
preserve
">IN Propoſitione 48: </
s
>
<
s
xml:id
="
echoid-s9156
"
xml:space
="
preserve
">ſumatur de figura Propoſit. </
s
>
<
s
xml:id
="
echoid-s9157
"
xml:space
="
preserve
">46. </
s
>
<
s
xml:id
="
echoid-s9158
"
xml:space
="
preserve
">parabola.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s9159
"
xml:space
="
preserve
">ZAG, cum baſi, ZG, & </
s
>
<
s
xml:id
="
echoid-s9160
"
xml:space
="
preserve
">axi, AQ, & </
s
>
<
s
xml:id
="
echoid-s9161
"
xml:space
="
preserve
">axi, AQ, & </
s
>
<
s
xml:id
="
echoid-s9162
"
xml:space
="
preserve
">reſecto eius minori fruſto,
<
lb
/>
DPG, de eiuſdem figura adnuc ſumatur, AXG, trilineum, in quo
<
lb
/>
ducitur, DE, æquidiſtans ipſi, AX, & </
s
>
<
s
xml:id
="
echoid-s9163
"
xml:space
="
preserve
">ſeorſim ponatur, vt autem fiat
<
lb
/>
<
figure
xlink:label
="
fig-0382-01
"
xlink:href
="
fig-0382-01a
"
number
="
261
">
<
image
file
="
0382-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0382-01
"/>
</
figure
>
ſolitum exemplum, reuoluatur parabola, ZAG, circa manentem
<
lb
/>
axim, AQ, & </
s
>
<
s
xml:id
="
echoid-s9164
"
xml:space
="
preserve
">fruſtum minus eiuſdem, quod eſt, DPG, circa, DP,
<
lb
/>
ex quo fiat aceruus minor, RDG. </
s
>
<
s
xml:id
="
echoid-s9165
"
xml:space
="
preserve
">Inſuper trilineum, AXG, reuo-
<
lb
/>
luatur circa, GX, vt fiat apex parabolicus, AGZ, & </
s
>
<
s
xml:id
="
echoid-s9166
"
xml:space
="
preserve
">ex GDE, eius
<
lb
/>
fruſtum, GDY; </
s
>
<
s
xml:id
="
echoid-s9167
"
xml:space
="
preserve
">patet igitur ex ipſa Prop. </
s
>
<
s
xml:id
="
echoid-s9168
"
xml:space
="
preserve
">48. </
s
>
<
s
xml:id
="
echoid-s9169
"
xml:space
="
preserve
">aceruum minorem,
<
lb
/>
RDG, ad conoidem parabolicam, ZAG, habere rationem compo-
<
lb
/>
ſitam ex ea, quam habet compoſita ex {1/3}. </
s
>
<
s
xml:id
="
echoid-s9170
"
xml:space
="
preserve
">ZP, & </
s
>
<
s
xml:id
="
echoid-s9171
"
xml:space
="
preserve
">{1/6}. </
s
>
<
s
xml:id
="
echoid-s9172
"
xml:space
="
preserve
">PG, ad, ZP, & </
s
>
<
s
xml:id
="
echoid-s9173
"
xml:space
="
preserve
">
<
lb
/>
ex ratione parallelepipedi ſub, DP, & </
s
>
<
s
xml:id
="
echoid-s9174
"
xml:space
="
preserve
">quadrato, PG, ad dimidium
<
lb
/>
parallelepipedi ſub, AQ & </
s
>
<
s
xml:id
="
echoid-s9175
"
xml:space
="
preserve
">quadrato, QG; </
s
>
<
s
xml:id
="
echoid-s9176
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s9177
"
xml:space
="
preserve
">ſic etiã eſſe quodlibet
<
lb
/>
ſolidum ſimilare genitum ex fruſto parabolæ, DGP, ad ſibi ſimila-
<
lb
/>
re genitum ex ſemiparabola, AQG; </
s
>
<
s
xml:id
="
echoid-s9178
"
xml:space
="
preserve
">iuxta communem regulam,
<
lb
/>
ZG. </
s
>
<
s
xml:id
="
echoid-s9179
"
xml:space
="
preserve
">Item ex eadem Prop. </
s
>
<
s
xml:id
="
echoid-s9180
"
xml:space
="
preserve
">patet apicem parabolicum, AGZ, ad
<
lb
/>
eius fruſtum, DGY, habere rationem compoſitam ex ea, quam
<
lb
/>
habet ſexta pars parallelepipedi ſub AQ, & </
s
>
<
s
xml:id
="
echoid-s9181
"
xml:space
="
preserve
">quadrato, QG, ad pa-
<
lb
/>
rallelepipedum ſub, DP, & </
s
>
<
s
xml:id
="
echoid-s9182
"
xml:space
="
preserve
">quadrato, PG, & </
s
>
<
s
xml:id
="
echoid-s9183
"
xml:space
="
preserve
">ex ea, quam habet,
<
lb
/>
ZP, ad reſiduum, demptis ab eadem, ZP, {2/3}. </
s
>
<
s
xml:id
="
echoid-s9184
"
xml:space
="
preserve
">ZP, cum {1/6}. </
s
>
<
s
xml:id
="
echoid-s9185
"
xml:space
="
preserve
">PG: </
s
>
<
s
xml:id
="
echoid-s9186
"
xml:space
="
preserve
">Sic
<
lb
/>
autem quoque erit quodcunque ſolidum ſimilare genitum ex trili-
<
lb
/>
neo, AXG, ad ſibi ſimilare genitum ex trilineo, GDE, iuxta com-
<
lb
/>
munem regulam, AX.</
s
>
<
s
xml:id
="
echoid-s9187
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
</
text
>
</
echo
>