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
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
<
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
="
039/01/189.jpg
"
pagenum
="
161
"/>
ris periodici inverſe: patet hanc rationem compoſitam diminui per </
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
arrow.to.target
n
="
note137
"/>
actionem vis
<
emph
type
="
italics
"/>
KL,
<
emph.end
type
="
italics
"/>
adeoque tempus periodicum, ſi maneat Orbis
<
lb
/>
radius
<
emph
type
="
italics
"/>
TP,
<
emph.end
type
="
italics
"/>
augeri, idQ.E.I. ſubduplicata ratione qua vis illa cen
<
lb
/>
tripeta diminuitur: auctoque adeo vel diminuto hoc Radio, tem
<
lb
/>
pus periodicum augeri magis, vel diminui minus quam in Radii hu
<
lb
/>
jus ratione ſeſquiplicata, per Corol. </
s
>
<
s
>6. Prop. </
s
>
<
s
>IV. </
s
>
<
s
>Si vis illa corporis
<
lb
/>
centralis paulatim langueſceret, corpus
<
emph
type
="
italics
"/>
P
<
emph.end
type
="
italics
"/>
minus ſemper & minus
<
lb
/>
attractum perpetuo recederet longius a centro
<
emph
type
="
italics
"/>
T
<
emph.end
type
="
italics
"/>
; & contra, ſi vis
<
lb
/>
illa augeretur, accederet propius. </
s
>
<
s
>Ergo ſi actio corporis longin
<
lb
/>
qui
<
emph
type
="
italics
"/>
S,
<
emph.end
type
="
italics
"/>
qua vis illa diminuitur, augeatur ac diminuatur per vices;
<
lb
/>
augebitur ſimul ac diminuetur Radius
<
emph
type
="
italics
"/>
TP
<
emph.end
type
="
italics
"/>
per vices, & tempus pe
<
lb
/>
riodicum augebitur ac diminuetur in ratione compoſita ex ratione
<
lb
/>
ſeſquiplicata Radii & ratione ſubduplicata qua vis illa centripeta
<
lb
/>
corporis centralis
<
emph
type
="
italics
"/>
T,
<
emph.end
type
="
italics
"/>
per incrementum vel decrementum actionis
<
lb
/>
corporis longinqui
<
emph
type
="
italics
"/>
S,
<
emph.end
type
="
italics
"/>
diminuitur vel augetur. </
s
>
</
p
>
<
p
type
="
margin
">
<
s
>
<
margin.target
id
="
note137
"/>
LIBER
<
lb
/>
PRIMUS.</
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
emph
type
="
italics
"/>
Corol.
<
emph.end
type
="
italics
"/>
7. Ex præmiſſis conſequitur etiam quod Ellipſeos a cor
<
lb
/>
pore
<
emph
type
="
italics
"/>
P
<
emph.end
type
="
italics
"/>
deſcriptæ Axis, ſeu Apſidum linea, quoad motum angula
<
lb
/>
rem progreditur & regreditur per vices, ſed magis tamen progre
<
lb
/>
ditur, & in ſingulis corporis revolutionibus per exceſſum progreſ
<
lb
/>
ſionis fertur in conſequentia. </
s
>
<
s
>Nam vis qua corpus
<
emph
type
="
italics
"/>
P
<
emph.end
type
="
italics
"/>
urgetur in
<
lb
/>
corpus
<
emph
type
="
italics
"/>
T
<
emph.end
type
="
italics
"/>
in Quadraturis, ubi vis
<
emph
type
="
italics
"/>
MN
<
emph.end
type
="
italics
"/>
evanuit, componitur ex vi
<
lb
/>
<
emph
type
="
italics
"/>
LM
<
emph.end
type
="
italics
"/>
& vi centripeta qua corpus
<
emph
type
="
italics
"/>
T
<
emph.end
type
="
italics
"/>
trahit corpus
<
emph
type
="
italics
"/>
P.
<
emph.end
type
="
italics
"/>
Vis prior
<
emph
type
="
italics
"/>
LM,
<
emph.end
type
="
italics
"/>
<
lb
/>
ſi augeatur diſtantia
<
emph
type
="
italics
"/>
PT,
<
emph.end
type
="
italics
"/>
augetur in eadem fere ratione cum hac
<
lb
/>
diſtantia, & vis poſterior decreſcit in duplicata illa ratione, adeo
<
lb
/>
que ſumma harum virium decreſcit in minore quam duplicata ra
<
lb
/>
tione diſtantiæ
<
emph
type
="
italics
"/>
PT,
<
emph.end
type
="
italics
"/>
& propterea (per Corol. </
s
>
<
s
>1. Prop. </
s
>
<
s
>XLV) efficit
<
lb
/>
ut Aux, ſeu Apſis ſumma, regrediatur. </
s
>
<
s
>In Conjunctione vero &
<
lb
/>
Oppoſitione, vis qua corpus
<
emph
type
="
italics
"/>
P
<
emph.end
type
="
italics
"/>
urgetur in corpus
<
emph
type
="
italics
"/>
T
<
emph.end
type
="
italics
"/>
differentia eſt
<
lb
/>
inter vim qua corpus
<
emph
type
="
italics
"/>
T
<
emph.end
type
="
italics
"/>
trahit corpus
<
emph
type
="
italics
"/>
P
<
emph.end
type
="
italics
"/>
& vim
<
emph
type
="
italics
"/>
KL
<
emph.end
type
="
italics
"/>
; & differen
<
lb
/>
tia illa, propterea quod vis
<
emph
type
="
italics
"/>
KL
<
emph.end
type
="
italics
"/>
augetur quamproxime in ratione
<
lb
/>
diſtantiæ
<
emph
type
="
italics
"/>
PT,
<
emph.end
type
="
italics
"/>
decreſcit in majore quam duplicata ratione diſtan
<
lb
/>
tiæ
<
emph
type
="
italics
"/>
PT,
<
emph.end
type
="
italics
"/>
adeoque (per Corol. </
s
>
<
s
>1. Prop.XLV) efficit ut Aux progre
<
lb
/>
diatur. </
s
>
<
s
>In locis inter Syzygias & Quadraturas pendet motus Au
<
lb
/>
gis ex cauſa utraque conjunctim, adeo ut pro hujus vel alterius
<
lb
/>
exceſſu progrediatur ipſa vel regrediatur. </
s
>
<
s
>Unde cum vis
<
emph
type
="
italics
"/>
KL
<
emph.end
type
="
italics
"/>
in
<
lb
/>
Syzygiis ſit quaſi duplo major quam vis
<
emph
type
="
italics
"/>
LM
<
emph.end
type
="
italics
"/>
in Quadraturis, ex
<
lb
/>
ceſſus in tota revolutione erit penes vim
<
emph
type
="
italics
"/>
KL,
<
emph.end
type
="
italics
"/>
transferetque Au
<
lb
/>
gem ſingulis revolutionibus in conſequentia. </
s
>
<
s
>Veritas autem hujus
<
lb
/>
& præcedentis Corollarii facilius intelligetur concipiendo Syſtema
<
lb
/>
corporum duorum
<
emph
type
="
italics
"/>
T, P
<
emph.end
type
="
italics
"/>
corporibus pluribus
<
emph
type
="
italics
"/>
S, S, S,
<
emph.end
type
="
italics
"/>
&c, in Or
<
lb
/>
be
<
emph
type
="
italics
"/>
ESE
<
emph.end
type
="
italics
"/>
conſiſtentibus, undique cingi. </
s
>
<
s
>Namque horum actioni-</
s
>
</
p
>
</
subchap2
>
</
subchap1
>
</
chap
>
</
body
>
</
text
>
</
archimedes
>