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
="
039/01/374.jpg
"
pagenum
="
346
"/>
<
arrow.to.target
n
="
note354
"/>
minor ex parte concava quam ex parte convexa; prævalebit im
<
lb
/>
preſſio fortior, & motum Orbis vel accelerabit vel retardabit,
<
lb
/>
prout in eandem regionem cum ipſius motu vel in contrariam di
<
lb
/>
rigitur. </
s
>
<
s
>Proinde ut Orbis unuſquiſQ.E.I. motu ſuo uniformiter
<
lb
/>
perſeveret, debent impreſſiones ex parte utraque ſibi invicem æqua
<
lb
/>
ri, & fieri in regiones contrarias. </
s
>
<
s
>Unde cum impreſſiones ſunt ut
<
lb
/>
contiguæ ſuperficies & harum tranſlationes ab invicem, erunt tran
<
lb
/>
ſlationes inverſe ut ſuperficies, hoc eſt, inverſe ut ſuperficierum di
<
lb
/>
ſtantiæ ab axe. </
s
>
<
s
>Sunt autem differentiæ motuum angularium circa
<
lb
/>
axem ut hæ tranſlationes applicatæ ad diſtantias, ſive ut tranſlati
<
lb
/>
ones directe & diſtantiæ inverſe; hoc eſt (conjunctis rationibus)
<
lb
/>
ut quadrata diſtantiarum inverſe. </
s
>
<
s
>Quare ſi ad infinitæ rectæ
<
lb
/>
<
emph
type
="
italics
"/>
SABCDEQ
<
emph.end
type
="
italics
"/>
partes ſin
<
lb
/>
<
figure
id
="
id.039.01.374.1.jpg
"
xlink:href
="
039/01/374/1.jpg
"
number
="
201
"/>
<
lb
/>
gulas erigantur perpendicula
<
lb
/>
<
emph
type
="
italics
"/>
Aa, Bb, Cc, Dd, Ee,
<
emph.end
type
="
italics
"/>
&c. </
s
>
<
s
>
<
lb
/>
ipſarum
<
emph
type
="
italics
"/>
SA, SB, SC, SD,
<
lb
/>
SE,
<
emph.end
type
="
italics
"/>
&c. </
s
>
<
s
>quadratis reciproce
<
lb
/>
proportionalia, & per ter
<
lb
/>
minos perpendicularium du
<
lb
/>
ci intelligatur linea curva
<
lb
/>
Hyperbolica; erunt ſummæ
<
lb
/>
differentiarum, hoc eſt, mo
<
lb
/>
tus toti angulares, ut re
<
lb
/>
ſpondentes ſummæ linearum
<
lb
/>
<
emph
type
="
italics
"/>
Aa, Bb, Cc, Dd, Ee
<
emph.end
type
="
italics
"/>
: id
<
lb
/>
eſt, ſi ad conſtituendum Me
<
lb
/>
dium uniformiter fluidum, Orbium numerus augeatur & latitudo
<
lb
/>
minuatur in infinitum, ut areæ Hyperbolicæ his ſummis analogæ
<
lb
/>
<
emph
type
="
italics
"/>
AaQ, BbQ, CcQ, DdQ, EeQ,
<
emph.end
type
="
italics
"/>
&c. </
s
>
<
s
>Et tempora motibus an
<
lb
/>
gularibus reciproce proportionalia, erunt etiam his areis reciproce
<
lb
/>
proportionalia. </
s
>
<
s
>Eſt igitur tempus periodicum particulæ cujuſvis
<
lb
/>
<
emph
type
="
italics
"/>
D
<
emph.end
type
="
italics
"/>
reciproce ut area
<
emph
type
="
italics
"/>
DdQ,
<
emph.end
type
="
italics
"/>
hoc eſt, (per notas Curvarum qua
<
lb
/>
draturas) directe ut diſtantia
<
emph
type
="
italics
"/>
SD. Q.E.D.
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
<
p
type
="
margin
">
<
s
>
<
margin.target
id
="
note354
"/>
DE MOTU
<
lb
/>
CORPORUM</
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
emph
type
="
italics
"/>
Corol.
<
emph.end
type
="
italics
"/>
1. Hinc motus angulares particularum fluidi ſunt reci
<
lb
/>
proce ut ipſarum diſtantiæ ab axe cylindri, & velocitates abſo
<
lb
/>
lutæ ſunt æquales. </
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
emph
type
="
italics
"/>
Corol.
<
emph.end
type
="
italics
"/>
2. Si fluidum in vaſe cylindrico longitudinis infinitæ con
<
lb
/>
tineatur, & cylindrum alium interiorem contineat, revolvatur
<
lb
/>
autem cylindrus uterque circa axem communem, ſintque revolu-</
s
>
</
p
>
</
subchap2
>
</
subchap1
>
</
chap
>
</
body
>
</
text
>
</
archimedes
>