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
|<
<
(311)
of 569
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div743
"
type
="
section
"
level
="
1
"
n
="
438
">
<
pb
o
="
311
"
file
="
0331
"
n
="
331
"
rhead
="
LIBER IV.
"/>
</
div
>
<
div
xml:id
="
echoid-div745
"
type
="
section
"
level
="
1
"
n
="
439
">
<
head
xml:id
="
echoid-head459
"
xml:space
="
preserve
">COROLLARIVM.</
head
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s7489
"
xml:space
="
preserve
">_H_Incliquet, ſi cuilibetparallelogrammo eſt inſcriptibilis ſemip. </
s
>
<
s
xml:id
="
echoid-s7490
"
xml:space
="
preserve
">1.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s7491
"
xml:space
="
preserve
">rabola talipacto, quo dictum eſt, quod parietates, quæ paralle-
<
lb
/>
logrammis contingunt, etiam ipſis parabolis competere poſſunt.</
s
>
<
s
xml:id
="
echoid-s7492
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div746
"
type
="
section
"
level
="
1
"
n
="
440
">
<
head
xml:id
="
echoid-head460
"
xml:space
="
preserve
">THEOREMA XX. PROPOS. XXI.</
head
>
<
p
>
<
s
xml:id
="
echoid-s7493
"
xml:space
="
preserve
">O Mnia quadrata parallelogrammi in eadem baſi, & </
s
>
<
s
xml:id
="
echoid-s7494
"
xml:space
="
preserve
">cir-
<
lb
/>
ca eundem axim, vel diametrum cum parabola, regu-
<
lb
/>
la baſi, ſunt dupla omnium quadratorum ipſius parabolæ:
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s7495
"
xml:space
="
preserve
">Omnia verò quadrata parabolæ ſunt fexquialtera omnium
<
lb
/>
quadratorum trianguli in eadem baſi, & </
s
>
<
s
xml:id
="
echoid-s7496
"
xml:space
="
preserve
">circa eundem axim,
<
lb
/>
vel diametrum cum ipſa conſtituti.</
s
>
<
s
xml:id
="
echoid-s7497
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s7498
"
xml:space
="
preserve
">Sit ergo parabola, cuius baſis, VF, axis, vel diameter, EM,
<
lb
/>
<
figure
xlink:label
="
fig-0331-01
"
xlink:href
="
fig-0331-01a
"
number
="
222
">
<
image
file
="
0331-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0331-01
"/>
</
figure
>
ſit etiam parallelogrammum,
<
lb
/>
AF, & </
s
>
<
s
xml:id
="
echoid-s7499
"
xml:space
="
preserve
">triangulum, EVF, in
<
lb
/>
eadem baſi, VF, & </
s
>
<
s
xml:id
="
echoid-s7500
"
xml:space
="
preserve
">circa eun-
<
lb
/>
dem axim, vel diametrum, EM.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s7501
"
xml:space
="
preserve
">Dico, omnia quadrata, AF, re-
<
lb
/>
gula, VF, omnium quadrato-
<
lb
/>
rum parabolæ, VEF, effe du-
<
lb
/>
pla: </
s
>
<
s
xml:id
="
echoid-s7502
"
xml:space
="
preserve
">Omnia verò quadrata para-
<
lb
/>
bolæ, VEF, omnium quadra-
<
lb
/>
torum trianguli, VEF, effe fex-
<
lb
/>
quialtera. </
s
>
<
s
xml:id
="
echoid-s7503
"
xml:space
="
preserve
">Sumaturintra, EM,
<
lb
/>
vtcunque punctum, N, per quodipſi, VF, agatur parallela, ND,
<
lb
/>
ſecans curuam parabolę; </
s
>
<
s
xml:id
="
echoid-s7504
"
xml:space
="
preserve
">in, O; </
s
>
<
s
xml:id
="
echoid-s7505
"
xml:space
="
preserve
">eſt ergo quadratum, MF, vel qua-
<
lb
/>
dratum, ND, ad quadratum, NO, vt, ME, ad, EN, eſt au-
<
lb
/>
tem, EF, parallelogrammum in eadem baſi, & </
s
>
<
s
xml:id
="
echoid-s7506
"
xml:space
="
preserve
">altitudine cumſe-
<
lb
/>
miparabola, EMF, regula eſt, MF, & </
s
>
<
s
xml:id
="
echoid-s7507
"
xml:space
="
preserve
">punctum, N, ſumptum vt-
<
lb
/>
cunque, per quod regulæ parallela ducta eſt, ND, repertumq; </
s
>
<
s
xml:id
="
echoid-s7508
"
xml:space
="
preserve
">eſt,
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0331-01
"
xlink:href
="
note-0331-01a
"
xml:space
="
preserve
">Coroll. 3.
<
lb
/>
16. 1. 2.</
note
>
vt quadratum, DN, ad quadratum, NO, ita eſte, ME, ad EN,
<
lb
/>
ergo horum quatuor ordinum magnitudines erunt proportionales
<
lb
/>
collectæ iuxta dictas quatuor magnitudines proportionales ſci-
<
lb
/>
licet omnia quadrata, EF, magnitudines primi ordinis collectæ
<
lb
/>
iuxta primam ſcilicet iuxta quadratum, ND, ad omnia quadrata
<
lb
/>
femiparabolæ, EMF, magnitudines fecundi ordims collectas
<
lb
/>
iuxta ſecundam ſcilicet iuxta quadratum, NO, erunt vt </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>