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: 152
[Note]
Page: 153
[Note]
Page: 153
[Note]
Page: 154
[Note]
Page: 154
[Note]
Page: 155
[Note]
Page: 155
[Note]
Page: 155
[Note]
Page: 155
[Note]
Page: 155
[Note]
Page: 155
[Note]
Page: 156
[Note]
Page: 156
[Note]
Page: 157
[Note]
Page: 157
[Note]
Page: 157
[Note]
Page: 157
[Note]
Page: 158
[Note]
Page: 158
[Note]
Page: 158
[Note]
Page: 159
[Note]
Page: 159
[Note]
Page: 159
[Note]
Page: 159
[Note]
Page: 161
[Note]
Page: 161
[Note]
Page: 161
[Note]
Page: 161
[Note]
Page: 161
[Note]
Page: 162
<
1 - 8
[out of range]
>
page
|<
<
(412)
of 569
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div962
"
type
="
section
"
level
="
1
"
n
="
573
">
<
p
>
<
s
xml:id
="
echoid-s10759
"
xml:space
="
preserve
">
<
pb
o
="
412
"
file
="
0432
"
n
="
432
"
rhead
="
GEOMETRIÆ
"/>
ad ſibi ſimilare genitum ex triangulo, DBF, iuxta communem re-
<
lb
/>
gulam, DF.</
s
>
<
s
xml:id
="
echoid-s10760
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div963
"
type
="
section
"
level
="
1
"
n
="
574
">
<
head
xml:id
="
echoid-head599
"
xml:space
="
preserve
">SCHOLIVM.</
head
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s10761
"
xml:space
="
preserve
">_Q_V oniam verò ex Propoſ. </
s
>
<
s
xml:id
="
echoid-s10762
"
xml:space
="
preserve
">45. </
s
>
<
s
xml:id
="
echoid-s10763
"
xml:space
="
preserve
">Lib. </
s
>
<
s
xml:id
="
echoid-s10764
"
xml:space
="
preserve
">Primi habetur, quod ſi quæ
<
lb
/>
cunque conois byperbolica, im cuius baſi ſit cylindrus, & </
s
>
<
s
xml:id
="
echoid-s10765
"
xml:space
="
preserve
">conus
<
lb
/>
& </
s
>
<
s
xml:id
="
echoid-s10766
"
xml:space
="
preserve
">circa eundem axem, vel diametrum ſecetur planis baſi æquidiſtan-
<
lb
/>
tibus, quibus pariter ſecentur cylindrus, & </
s
>
<
s
xml:id
="
echoid-s10767
"
xml:space
="
preserve
">conus, fient conceptæ in
<
lb
/>
ſolidis figuræ ſimiles baſi, ideò omnia plana eorundem regula baſi erũt
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0432-01
"
xlink:href
="
note-0432-01a
"
xml:space
="
preserve
">_45. l. 1._
<
lb
/>
_Elicitur ex_
<
lb
/>
_45. l. 1. pſo_
<
lb
/>
_Conoide_
<
lb
/>
_Hyperb. &_
<
lb
/>
_ex Cor. 3_
<
lb
/>
_34. l. 2. pro_
<
lb
/>
_Cylindro._
<
lb
/>
_& Cono-_</
note
>
omnes figuræ ſimiles dictorum ſolidorum, in quibus ſi ducatur pla-
<
lb
/>
num per axem, producet in ipſis figuras genitrices earundem, nempè
<
lb
/>
parallelogrammum in cylindro, hyperbolam in conoide, & </
s
>
<
s
xml:id
="
echoid-s10768
"
xml:space
="
preserve
">trian-
<
lb
/>
gulum in cono, dicta autem ſolida erunt ſimilaria genita ex his figu.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s10769
"
xml:space
="
preserve
">ris genitricibus iuxta communem regulam ipſam baſim, & </
s
>
<
s
xml:id
="
echoid-s10770
"
xml:space
="
preserve
">ideò eorũ
<
lb
/>
ratio nota erit, quia ſcimus quam rationem habeant inter ſe omnia
<
lb
/>
quadrata dictarum genitricium figurarum, regula baſi. </
s
>
<
s
xml:id
="
echoid-s10771
"
xml:space
="
preserve
">Hæc autem
<
lb
/>
ſimiliter pro ſequentibus memoria teneantùr, in quibus ſiet noſtrum
<
lb
/>
ſolitum exemplum per reuolutionem ſigurarum circa ſuos axes, Vt
<
lb
/>
habeamus omnes figuras ſimiles genitorum ſolidorum, quæ ſint circuli
<
lb
/>
diametros in figuris genitricibus, quibus ſint erecti, ſitas habentes,
<
lb
/>
licet eadem Verificentur ſſumptis non axibus, ſed tantum diametris,
<
lb
/>
Vt alibi pluriés repetitum eſt, ex dictis autem infraſcripta habentur
<
lb
/>
Corollaria.</
s
>
<
s
xml:id
="
echoid-s10772
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div965
"
type
="
section
"
level
="
1
"
n
="
575
">
<
head
xml:id
="
echoid-head600
"
xml:space
="
preserve
">COROLLARIVM I.</
head
>
<
p
>
<
s
xml:id
="
echoid-s10773
"
xml:space
="
preserve
">VTigitur fiat noſtrum exemplum in Prop. </
s
>
<
s
xml:id
="
echoid-s10774
"
xml:space
="
preserve
">1. </
s
>
<
s
xml:id
="
echoid-s10775
"
xml:space
="
preserve
">reuoluatur pa-
<
lb
/>
rallelogrammum, AF, circam manentem axim, BE, vt fiat
<
lb
/>
<
figure
xlink:label
="
fig-0432-01
"
xlink:href
="
fig-0432-01a
"
number
="
290
">
<
image
file
="
0432-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0432-01
"/>
</
figure
>
ex parallelogrammo, AF, cylindrus, A
<
lb
/>
F, ex hyperbola, DBF, conois, DBF,
<
lb
/>
& </
s
>
<
s
xml:id
="
echoid-s10776
"
xml:space
="
preserve
">ex triangulo, DBF, conus, DBF, col-
<
lb
/>
ligitur ergo cylindrum, AF, ad conoidé,
<
lb
/>
DBF, eſſe vt, OE, ad compoſitam ex,
<
lb
/>
NB, & </
s
>
<
s
xml:id
="
echoid-s10777
"
xml:space
="
preserve
">{1/3}. </
s
>
<
s
xml:id
="
echoid-s10778
"
xml:space
="
preserve
">BE, conoidem autem, DBF,
<
lb
/>
ad conum, DBF, eſſe vt compoſitam
<
lb
/>
ex ſexquialtera, OB, & </
s
>
<
s
xml:id
="
echoid-s10779
"
xml:space
="
preserve
">ex, BE, ad OE;
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s10780
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s10781
"
xml:space
="
preserve
">ita eſſe ſolida quæcunque ſimilaria
<
lb
/>
genita ex eiſdem figuris .</
s
>
<
s
xml:id
="
echoid-s10782
"
xml:space
="
preserve
">ſ. </
s
>
<
s
xml:id
="
echoid-s10783
"
xml:space
="
preserve
">ex parallelo-
<
lb
/>
grammo, AF, hyperbola, DBF, & </
s
>
<
s
xml:id
="
echoid-s10784
"
xml:space
="
preserve
">triã-
<
lb
/>
gulo, DBF, iuxta communem regulam,
<
lb
/>
DF, vt ſupra dictum eſt, quę declarare oportebat.</
s
>
<
s
xml:id
="
echoid-s10785
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
</
text
>
</
echo
>