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 Notes
<
1 - 8
[out of range]
>
[Note]
Page: 90
[Note]
Page: 90
[Note]
Page: 91
[Note]
Page: 91
[Note]
Page: 91
[Note]
Page: 91
[Note]
Page: 92
[Note]
Page: 92
[Note]
Page: 92
[Note]
Page: 92
[Note]
Page: 93
[Note]
Page: 93
[Note]
Page: 93
[Note]
Page: 93
[Note]
Page: 93
[Note]
Page: 93
[Note]
Page: 93
[Note]
Page: 93
[Note]
Page: 94
[Note]
Page: 94
[Note]
Page: 94
[Note]
Page: 94
[Note]
Page: 94
[Note]
Page: 94
[Note]
Page: 94
[Note]
Page: 95
[Note]
Page: 96
[Note]
Page: 96
[Note]
Page: 97
[Note]
Page: 97
<
1 - 8
[out of range]
>
page
|<
<
(244)
of 569
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div588
"
type
="
section
"
level
="
1
"
n
="
344
">
<
pb
o
="
244
"
file
="
0264
"
n
="
264
"
rhead
="
GEOMETRIÆ
"/>
</
div
>
<
div
xml:id
="
echoid-div590
"
type
="
section
"
level
="
1
"
n
="
345
">
<
head
xml:id
="
echoid-head362
"
xml:space
="
preserve
">THEOREMA XXIV. PROPOS. XXV.</
head
>
<
p
>
<
s
xml:id
="
echoid-s6033
"
xml:space
="
preserve
">IN figura circuli, & </
s
>
<
s
xml:id
="
echoid-s6034
"
xml:space
="
preserve
">ellipſis eiuſdem Theor. </
s
>
<
s
xml:id
="
echoid-s6035
"
xml:space
="
preserve
">21. </
s
>
<
s
xml:id
="
echoid-s6036
"
xml:space
="
preserve
">oſtenden-
<
lb
/>
dum eſt, ibi appoſitis retentis, ſumpta tamen vtcunque
<
lb
/>
portione minori, RFV, & </
s
>
<
s
xml:id
="
echoid-s6037
"
xml:space
="
preserve
">regula diametro eiuſdem portio-
<
lb
/>
nis. </
s
>
<
s
xml:id
="
echoid-s6038
"
xml:space
="
preserve
">ſ. </
s
>
<
s
xml:id
="
echoid-s6039
"
xml:space
="
preserve
">FM; </
s
>
<
s
xml:id
="
echoid-s6040
"
xml:space
="
preserve
">omnia quadrata parallelogrammi, Δ V, ad omnia
<
lb
/>
quadrata portionis, RFV, eſſe vt quadratum, FM, ad ſpa-
<
lb
/>
tium, quod remanet, dempto rectangulo ſub, IM, & </
s
>
<
s
xml:id
="
echoid-s6041
"
xml:space
="
preserve
">ſub, F
<
lb
/>
M, (ad quam, FM, ſit, vt, Δ V, ad portionem, RFV,) à re-
<
lb
/>
ctangulo ſub, FM, & </
s
>
<
s
xml:id
="
echoid-s6042
"
xml:space
="
preserve
">ſub, {2/3}, ipſius, MH.</
s
>
<
s
xml:id
="
echoid-s6043
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s6044
"
xml:space
="
preserve
">Sit igitur vt, Δ V, ad, RFV, ita, FM, ad, MI; </
s
>
<
s
xml:id
="
echoid-s6045
"
xml:space
="
preserve
">omnia ergo qua-
<
lb
/>
drata, Δ V, adrectangula ſub, Δ V, VT, ſunt vt quadratum, FM,
<
lb
/>
ad rectangulum, FMI, rectangula inſuper ſub, Δ V, VT, ad re-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0264-01
"
xlink:href
="
note-0264-01a
"
xml:space
="
preserve
">14. Lib. 2.</
note
>
ctangula ſub portione, RFV, & </
s
>
<
s
xml:id
="
echoid-s6046
"
xml:space
="
preserve
">ſub, VT, ſunt vt, Δ V, ad portionem,
<
lb
/>
<
figure
xlink:label
="
fig-0264-01
"
xlink:href
="
fig-0264-01a
"
number
="
163
">
<
image
file
="
0264-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0264-01
"/>
</
figure
>
RFV, .</
s
>
<
s
xml:id
="
echoid-s6047
"
xml:space
="
preserve
">i. </
s
>
<
s
xml:id
="
echoid-s6048
"
xml:space
="
preserve
">vt, FM, ad, MT, .</
s
>
<
s
xml:id
="
echoid-s6049
"
xml:space
="
preserve
">i. </
s
>
<
s
xml:id
="
echoid-s6050
"
xml:space
="
preserve
">ſumpta, MI,
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0264-02
"
xlink:href
="
note-0264-02a
"
xml:space
="
preserve
">Coroll. 1.
<
lb
/>
26. lib. 2.</
note
>
communi altitudine, vt rectangulum, F
<
lb
/>
MI, ad rectangulum, r MI, ergo ex æ-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0264-03
"
xlink:href
="
note-0264-03a
"
xml:space
="
preserve
">@. Lib. 2.</
note
>
quali omnia quadrata, Δ V, ad rectangu-
<
lb
/>
la ſub portione, RFV, & </
s
>
<
s
xml:id
="
echoid-s6051
"
xml:space
="
preserve
">ſub, VT, erunt
<
lb
/>
vt quadratum, FM, ad rectangulum,
<
lb
/>
Γ Μ Ι, quod ſerua.</
s
>
<
s
xml:id
="
echoid-s6052
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s6053
"
xml:space
="
preserve
">Vlterius omnia quadrata, ΔV, ad om-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0264-04
"
xlink:href
="
note-0264-04a
"
xml:space
="
preserve
">@. Lib. 2.</
note
>
nia quadrata, VII, ſunt vt quadratum, F
<
lb
/>
M, ad quadratum, MO, vel ad quadra-
<
lb
/>
tum, RV, .</
s
>
<
s
xml:id
="
echoid-s6054
"
xml:space
="
preserve
">i. </
s
>
<
s
xml:id
="
echoid-s6055
"
xml:space
="
preserve
">ad quatuor rectangula ſub,
<
lb
/>
R M, MV: </
s
>
<
s
xml:id
="
echoid-s6056
"
xml:space
="
preserve
">Omnia inſuper quadrata,
<
lb
/>
V II, ad rectangula ſub portione, RFV,
<
lb
/>
& </
s
>
<
s
xml:id
="
echoid-s6057
"
xml:space
="
preserve
">quadrilineo, RTHY V, ſunt vt ſex
<
lb
/>
quadrata, CE, ad quadratũ, FH, nam in
<
lb
/>
circulo omnia quadrata, RZ, ſunt ſex-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0264-05
"
xlink:href
="
note-0264-05a
"
xml:space
="
preserve
">Elicitur
<
lb
/>
èx 21.hu-
<
lb
/>
ius.</
note
>
cupla rectangulorum ſub portione, RF
<
lb
/>
V, & </
s
>
<
s
xml:id
="
echoid-s6058
"
xml:space
="
preserve
">quadrilineo, RTHYV, & </
s
>
<
s
xml:id
="
echoid-s6059
"
xml:space
="
preserve
">ideo ſunt
<
lb
/>
ad illa, vt ſex quadrata, CE, ad quadra-
<
lb
/>
tum, CE, vel ad quadratum, FH, in ellipſi
<
lb
/>
verò omnia quadrata, RZ, ſunt ad re-
<
lb
/>
ctangula ſub portione, RFV, & </
s
>
<
s
xml:id
="
echoid-s6060
"
xml:space
="
preserve
">quadrilineo, RTHYV, vt ſex quadra-
<
lb
/>
ta, CE, ad quadratum, FH, quod elicitur ex Prop. </
s
>
<
s
xml:id
="
echoid-s6061
"
xml:space
="
preserve
">21. </
s
>
<
s
xml:id
="
echoid-s6062
"
xml:space
="
preserve
">huius. </
s
>
<
s
xml:id
="
echoid-s6063
"
xml:space
="
preserve
">Quia
<
lb
/>
vero rectangulum, RMV, ad rectangulum, FMH, (tum in cir-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0264-06
"
xlink:href
="
note-0264-06a
"
xml:space
="
preserve
">17. 3. Con.</
note
>
</
s
>
</
p
>
</
div
>
</
text
>
</
echo
>