Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
Text
Text Image
Image
XML
Thumbnail overview
Document information
None
Concordance
Figures
Thumbnails
page
|<
<
of 524
>
>|
<
archimedes
>
<
text
>
<
body
>
<
chap
>
<
subchap1
>
<
subchap2
>
<
p
type
="
main
">
<
s
>
<
pb
xlink:href
="
039/01/290.jpg
"
pagenum
="
262
"/>
<
arrow.to.target
n
="
note238
"/>
</
s
>
</
p
>
<
p
type
="
margin
">
<
s
>
<
margin.target
id
="
note238
"/>
DE MOTU
<
lb
/>
CORPORUM</
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
emph
type
="
italics
"/>
Corol.
<
emph.end
type
="
italics
"/>
Unde nec motus partium fluidi inter ſe, per preſſionem
<
lb
/>
fluido ubivis in externa ſuperficie illatam, mutari poſſunt, niſi qua
<
lb
/>
tenus aut figura ſuperficiei alicubi mutatur, aut omnes fluidi partes
<
lb
/>
intenſius vel remiſſius ſeſe premendo difficilius vel facilius labun
<
lb
/>
tur inter ſe. </
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
emph
type
="
center
"/>
PROPOSITIO XX. THEOREMA XV.
<
emph.end
type
="
center
"/>
</
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
emph
type
="
italics
"/>
Si Fluidi Sphærici, & in æqualibus a centro diſtantiis homogenei,
<
lb
/>
fundo Sphærico concentrico incumbentis partes ſingulæ verſus
<
lb
/>
centrum totius gravitent; ſuſtinet fundum pondus Cylindri, cu
<
lb
/>
jus bafis æqualis est ſuperficiei fundi, & altitudo eadem quæ
<
lb
/>
Fluidi incumbentis.
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
<
p
type
="
main
">
<
s
>Sit
<
emph
type
="
italics
"/>
DHM
<
emph.end
type
="
italics
"/>
ſuperficies ſundi, &
<
emph
type
="
italics
"/>
AEI
<
emph.end
type
="
italics
"/>
<
lb
/>
<
figure
id
="
id.039.01.290.1.jpg
"
xlink:href
="
039/01/290/1.jpg
"
number
="
169
"/>
<
lb
/>
ſuperficies ſuperior fluidi. </
s
>
<
s
>Superficiebus
<
lb
/>
ſphæricis innumeris
<
emph
type
="
italics
"/>
BFK, CGL
<
emph.end
type
="
italics
"/>
diſtin
<
lb
/>
guatur fluidum in Orbes concentricos æ
<
lb
/>
qualiter craſſos; & concipe vim gravita
<
lb
/>
tis agere ſolummodo in ſuperficiem ſupe
<
lb
/>
riorem Orbis cujuſque, & æquales eſſe a
<
lb
/>
ctiones in æquales partes ſuperficierum om
<
lb
/>
nium. </
s
>
<
s
>Premitur ergo ſuperficies ſuprema
<
lb
/>
<
emph
type
="
italics
"/>
AE
<
emph.end
type
="
italics
"/>
vi ſimplici gravitatis propriæ, qua &
<
lb
/>
omnes Orbis ſupremi partes & ſuperficies
<
lb
/>
ſecunda
<
emph
type
="
italics
"/>
BFK
<
emph.end
type
="
italics
"/>
(per Prop. </
s
>
<
s
>XIX.) pro menſura ſua æqualiter pre
<
lb
/>
muntur. </
s
>
<
s
>Premitur præterea ſuperficies ſecunda
<
emph
type
="
italics
"/>
BFK
<
emph.end
type
="
italics
"/>
vi propriæ
<
lb
/>
gravitatis, quæ addita vi priori facit preſſionem duplam. </
s
>
<
s
>Hac
<
lb
/>
preſſione, pro menſura ſua, & inſuper vi propriæ gravitatis, id eſt
<
lb
/>
preſſione tripla, urgetur ſuperficies tertia
<
emph
type
="
italics
"/>
CGL.
<
emph.end
type
="
italics
"/>
Et ſimiliter preſ
<
lb
/>
ſione quadrupla urgetur ſuperficies quarta, quintupla quinta, &
<
lb
/>
ſic deinceps. </
s
>
<
s
>Preſſio igitur qua ſuperficies unaquæque urgetur,
<
lb
/>
non eſt ut quantitas ſolida fluidi incumbentis, ſed ut numerus Or
<
lb
/>
bium ad uſque ſummitatem fluidi; & æquatur gravitati Orbis infi
<
lb
/>
mi multiplicatæ per numerum Orbium: hoc eſt, gravitati ſolidi cu
<
lb
/>
jus ultima ratio ad Cylindrum præfinitum, (ſi modo Orbium au
<
lb
/>
geatur numerus & minuatur craſſitudo in infinitum, ſic ut actio
<
lb
/>
gravitatis a ſuperficie infima ad ſupremam continua reddatur) fiet
<
lb
/>
ratio æqualitatis. </
s
>
<
s
>Suſtinet ergo ſuperficies infima pondus Cylindri </
s
>
</
p
>
</
subchap2
>
</
subchap1
>
</
chap
>
</
body
>
</
text
>
</
archimedes
>