Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
Text
Text Image
Image
XML
Thumbnail overview
Document information
None
Concordance
Figures
Thumbnails
Page concordance
<
1 - 30
31 - 60
61 - 90
91 - 120
121 - 150
151 - 180
181 - 210
211 - 240
241 - 270
271 - 300
301 - 330
331 - 360
361 - 390
391 - 420
421 - 450
451 - 480
481 - 510
511 - 524
>
Scan
Original
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
<
1 - 30
31 - 60
61 - 90
91 - 120
121 - 150
151 - 180
181 - 210
211 - 240
241 - 270
271 - 300
301 - 330
331 - 360
361 - 390
391 - 420
421 - 450
451 - 480
481 - 510
511 - 524
>
page
|<
<
of 524
>
>|
<
archimedes
>
<
text
>
<
body
>
<
chap
>
<
subchap1
>
<
subchap2
>
<
p
type
="
main
">
<
s
>
<
pb
xlink:href
="
039/01/337.jpg
"
pagenum
="
309
"/>
<
lb
/>
convexa erit verſus cataractam, & propterea major Cono cujus ba
<
lb
/>
<
arrow.to.target
n
="
note285
"/>
ſis eſt circellus ille
<
emph
type
="
italics
"/>
PQ
<
emph.end
type
="
italics
"/>
& altitudo
<
emph
type
="
italics
"/>
GH,
<
emph.end
type
="
italics
"/>
id eſt, major tertia parte
<
lb
/>
Cylindri eadem baſe & altitudine deſcripti. </
s
>
<
s
>Suſtinet autem cir
<
lb
/>
cellus ille pondus hujus columnæ, id eſt, pondus quod pondere
<
lb
/>
Coni ſeu tertiæ partis Cylindri illius majus eſt.
<
lb
/>
</
s
>
</
p
>
<
p
type
="
margin
">
<
s
>
<
margin.target
id
="
note285
"/>
LIBER
<
lb
/>
SECUNDUS.</
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
emph
type
="
italics
"/>
Corol.
<
emph.end
type
="
italics
"/>
8. Pondus aquæ quam circellus valde parvus
<
emph
type
="
italics
"/>
PQ
<
emph.end
type
="
italics
"/>
ſuſtinet,
<
lb
/>
minor eſt pondere duarum tertiarum partium Cylindri aquæ cujus
<
lb
/>
baſis eſt circellus ille & altitudo eſt
<
emph
type
="
italics
"/>
HG.
<
emph.end
type
="
italics
"/>
Nam ſtantibus jam po
<
lb
/>
ſitis, deſcribi intelligatur dimidium Sphæroidis cujus baſis eſt cir
<
lb
/>
cellus ille & ſemiaxis ſive altitudo eſt
<
emph
type
="
italics
"/>
HG.
<
emph.end
type
="
italics
"/>
Et hæc figura æqualis
<
lb
/>
erit duabus tertiis partibus Cylindri illius & comprehendet colum
<
lb
/>
nam aquæ congelatæ
<
emph
type
="
italics
"/>
PHQ
<
emph.end
type
="
italics
"/>
cujus pondus circellus ille ſuſtinet.
<
lb
/>
Nam ut motus aquæ ſit maxime directus, columnæ illius ſuper
<
lb
/>
ficies externa concurret cum baſi
<
emph
type
="
italics
"/>
PQ
<
emph.end
type
="
italics
"/>
in angulo nonnihil acuto,
<
lb
/>
propterea quod aqua cadendo perpetuo acceleratur & propter ac
<
lb
/>
celerationem fit tenuior; & cum angulus ille ſit recto minor, hæc
<
lb
/>
columna ad inferiores ejus partes jacebit intra dimidium Sphæroi
<
lb
/>
dis. </
s
>
<
s
>Eadem vero ſurſum acuta erit ſeu cuſpidata, ne horizontalis
<
lb
/>
motus aquæ ad verticem Sphæroidis ſit infinite velocior quam ejus
<
lb
/>
motus horizontem verſus. </
s
>
<
s
>Et quo minor eſt circellus
<
emph
type
="
italics
"/>
PQ
<
emph.end
type
="
italics
"/>
eo
<
lb
/>
acutior erit vertex columnæ; & circello in infinitum diminuto, an
<
lb
/>
gulus
<
emph
type
="
italics
"/>
PHQ
<
emph.end
type
="
italics
"/>
in infinitum diminuetur, & propterea columna ja
<
lb
/>
cebit intra dimidium Sphæroidis. </
s
>
<
s
>Eſt igitur columna illa minor
<
lb
/>
dimidio Sphæroidis, ſeu duabus tertiis partibus Cylindri cujus baſis
<
lb
/>
eſt circellus ille & altitudo
<
emph
type
="
italics
"/>
GH.
<
emph.end
type
="
italics
"/>
Suſtinet autem circellus vim aquæ
<
lb
/>
ponderi hujus columnæ æqualem, cum pondus aquæ ambientis in
<
lb
/>
defluxum ejus impendatur.
<
lb
/>
</
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
emph
type
="
italics
"/>
Corol.
<
emph.end
type
="
italics
"/>
9. Pondus aquæ quam circellus valde parvus
<
emph
type
="
italics
"/>
PQ
<
emph.end
type
="
italics
"/>
ſuſti
<
lb
/>
net, æquale ſet ponderi Cylindri aquæ cujus baſis eſt circellus ille
<
lb
/>
& altitudo eſt 1/2
<
emph
type
="
italics
"/>
GH
<
emph.end
type
="
italics
"/>
quamproxime. </
s
>
<
s
>Nam pondus hocce eſt me
<
lb
/>
dium Arithmeticum inter pondera Coni & Hemiſphæroidis præ
<
lb
/>
dictæ. At ſi circellus ille non ſit valde parvus, ſed augeatur donec
<
lb
/>
æquet foramen
<
emph
type
="
italics
"/>
EF
<
emph.end
type
="
italics
"/>
; hic ſuſtinebit pondus aquæ totius ſibi per
<
lb
/>
pendiculariter imminentis, id eſt, pondus Cylindri aquæ cujus ba
<
lb
/>
ſis eſt circellus ille & altitudo eſt
<
emph
type
="
italics
"/>
GH.
<
emph.end
type
="
italics
"/>
<
lb
/>
</
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
emph
type
="
italics
"/>
Corol.
<
emph.end
type
="
italics
"/>
10. Et (quantum ſentio) pondus quod circellus ſuſtinet,
<
lb
/>
eſt ſemper ad pondus Cylindri aquæ cujus baſis eſt circellus ille &
<
lb
/>
altitudo eſt 1/2
<
emph
type
="
italics
"/>
GH,
<
emph.end
type
="
italics
"/>
ut
<
emph
type
="
italics
"/>
EFq
<
emph.end
type
="
italics
"/>
ad
<
emph
type
="
italics
"/>
EFq
<
emph.end
type
="
italics
"/>
-1/2
<
emph
type
="
italics
"/>
PQq,
<
emph.end
type
="
italics
"/>
ſive ut circulus
<
lb
/>
<
emph
type
="
italics
"/>
EF
<
emph.end
type
="
italics
"/>
ad exceſſum circuli hujus ſupra ſemiſſem circelli
<
emph
type
="
italics
"/>
PQ
<
emph.end
type
="
italics
"/>
quam
<
lb
/>
proxime. </
s
>
</
p
>
</
subchap2
>
</
subchap1
>
</
chap
>
</
body
>
</
text
>
</
archimedes
>