Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
Text
Text Image
Image
XML
Thumbnail overview
Document information
None
Concordance
Figures
Thumbnails
List of thumbnails
<
1 - 10
11 - 20
21 - 30
31 - 40
41 - 50
51 - 60
61 - 70
71 - 80
81 - 90
91 - 100
101 - 110
111 - 120
121 - 130
131 - 140
141 - 150
151 - 160
161 - 170
171 - 180
181 - 190
191 - 200
201 - 210
211 - 220
221 - 230
231 - 240
241 - 250
251 - 260
261 - 270
271 - 280
281 - 290
291 - 300
301 - 310
311 - 320
321 - 330
331 - 340
341 - 350
351 - 360
361 - 370
371 - 380
381 - 390
391 - 400
401 - 410
411 - 420
421 - 430
431 - 440
441 - 450
451 - 460
461 - 470
471 - 480
481 - 490
491 - 500
501 - 510
511 - 520
521 - 524
>
201
202
203
204
205
206
207
208
209
210
<
1 - 10
11 - 20
21 - 30
31 - 40
41 - 50
51 - 60
61 - 70
71 - 80
81 - 90
91 - 100
101 - 110
111 - 120
121 - 130
131 - 140
141 - 150
151 - 160
161 - 170
171 - 180
181 - 190
191 - 200
201 - 210
211 - 220
221 - 230
231 - 240
241 - 250
251 - 260
261 - 270
271 - 280
281 - 290
291 - 300
301 - 310
311 - 320
321 - 330
331 - 340
341 - 350
351 - 360
361 - 370
371 - 380
381 - 390
391 - 400
401 - 410
411 - 420
421 - 430
431 - 440
441 - 450
451 - 460
461 - 470
471 - 480
481 - 490
491 - 500
501 - 510
511 - 520
521 - 524
>
page
|<
<
of 524
>
>|
<
archimedes
>
<
text
>
<
body
>
<
chap
>
<
subchap1
>
<
subchap2
>
<
p
type
="
main
">
<
s
>
<
pb
xlink:href
="
039/01/208.jpg
"
pagenum
="
180
"/>
<
arrow.to.target
n
="
note156
"/>
</
s
>
</
p
>
<
p
type
="
margin
">
<
s
>
<
margin.target
id
="
note156
"/>
DE MOTU
<
lb
/>
CORPORUM</
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
emph
type
="
italics
"/>
Corol.
<
emph.end
type
="
italics
"/>
5. Eadem valent ubi attractio oritur a Sphæræ utriuſque
<
lb
/>
virtute attractiva, mutuo exercita in Sphæram alteram. </
s
>
<
s
>Nam viri
<
lb
/>
bus ambabus geminatur attractio, proportione ſervata. </
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
emph
type
="
italics
"/>
Corol.
<
emph.end
type
="
italics
"/>
6. Si hujuſmodi Sphæræ aliquæ circa alias quieſcentes re
<
lb
/>
volvantur, ſingulæ circa ſingulas, ſintQ.E.D.ſtantiæ inter centra re
<
lb
/>
volventium & quieſcentium proportionales quieſcentium diame
<
lb
/>
tris; æqualia erunt Tempora periodica. </
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
emph
type
="
italics
"/>
Corol.
<
emph.end
type
="
italics
"/>
7. Et viciſſim, ſi Tempora periodica ſunt æqualia; diſtan
<
lb
/>
tiæ erunt proportionales diametris. </
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
emph
type
="
italics
"/>
Corol.
<
emph.end
type
="
italics
"/>
8. Eadem omnia, quæ ſuperius de motu corporum circa
<
lb
/>
umbilicos Conicarum Sectionum demonſtrata ſunt, obtinent ubi
<
lb
/>
Sphæra attrahens, formæ & conditionis cujuſvis jam deſcriptæ, lo
<
lb
/>
catur in umbilico. </
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
emph
type
="
italics
"/>
Corol.
<
emph.end
type
="
italics
"/>
9. Ut & ubi gyrantia ſunt etiam Sphæræ attrahentes, con
<
lb
/>
ditionis cujuſvis jam deſcriptæ. </
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
emph
type
="
center
"/>
PROPOSITIO LXXVII. THEOREMA XXXVII.
<
emph.end
type
="
center
"/>
</
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
emph
type
="
italics
"/>
Si ad ſingula Sphærarum puncta tendant vires centripetæ, proper
<
lb
/>
tionales diſtantiis punctorum a corporibus attractis: dico quod
<
lb
/>
vis compoſita, qua Sphæræ duæ ſe mutuo trahent, est ut di
<
lb
/>
ſtantia inter centra Sphærarum.
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
emph
type
="
italics
"/>
Cas.
<
emph.end
type
="
italics
"/>
1. Sit
<
emph
type
="
italics
"/>
AEBF
<
emph.end
type
="
italics
"/>
Sphæra,
<
emph
type
="
italics
"/>
S
<
emph.end
type
="
italics
"/>
<
lb
/>
<
figure
id
="
id.039.01.208.1.jpg
"
xlink:href
="
039/01/208/1.jpg
"
number
="
118
"/>
<
lb
/>
centrum ejus,
<
emph
type
="
italics
"/>
P
<
emph.end
type
="
italics
"/>
corpuſculum at
<
lb
/>
tractum,
<
emph
type
="
italics
"/>
PASB
<
emph.end
type
="
italics
"/>
axis Sphæræ per
<
lb
/>
centrum corpuſculi tranſiens,
<
emph
type
="
italics
"/>
EF,
<
lb
/>
ef
<
emph.end
type
="
italics
"/>
plana duo quibus Sphæra ſe
<
lb
/>
catur, huic axi perpendicularia &
<
lb
/>
hinc inde æqualiter diſtantia a
<
lb
/>
centro Sphæræ;
<
emph
type
="
italics
"/>
G, g
<
emph.end
type
="
italics
"/>
interſectio
<
lb
/>
nes planorum & axis, &
<
emph
type
="
italics
"/>
H
<
emph.end
type
="
italics
"/>
pun
<
lb
/>
ctum quodvis in plano
<
emph
type
="
italics
"/>
EF.
<
emph.end
type
="
italics
"/>
Pun
<
lb
/>
cti
<
emph
type
="
italics
"/>
H
<
emph.end
type
="
italics
"/>
vis centripeta in corpuſculum
<
emph
type
="
italics
"/>
P,
<
emph.end
type
="
italics
"/>
ſecundum lineam
<
emph
type
="
italics
"/>
PH
<
emph.end
type
="
italics
"/>
exer
<
lb
/>
cita, eſt ut diſtantia
<
emph
type
="
italics
"/>
PH
<
emph.end
type
="
italics
"/>
; & (per Legum Corol. </
s
>
<
s
>2.) ſecundum li
<
lb
/>
neam
<
emph
type
="
italics
"/>
PG,
<
emph.end
type
="
italics
"/>
ſeu verſus centrum
<
emph
type
="
italics
"/>
S,
<
emph.end
type
="
italics
"/>
ut longitudo
<
emph
type
="
italics
"/>
PG.
<
emph.end
type
="
italics
"/>
Igitur pun
<
lb
/>
ctorum omnium in plano
<
emph
type
="
italics
"/>
EF,
<
emph.end
type
="
italics
"/>
hoc eſt plani totius vis, qua corpuſ
<
lb
/>
culum
<
emph
type
="
italics
"/>
P
<
emph.end
type
="
italics
"/>
trahitur verſus centrum
<
emph
type
="
italics
"/>
S,
<
emph.end
type
="
italics
"/>
eſt ut numerus punctorum
<
lb
/>
ductus in diſtantiam
<
emph
type
="
italics
"/>
PG:
<
emph.end
type
="
italics
"/>
id eſt, ut contentum ſub plano ipſo
<
emph
type
="
italics
"/>
EF
<
emph.end
type
="
italics
"/>
<
lb
/>
& diſtantia illa
<
emph
type
="
italics
"/>
PG.
<
emph.end
type
="
italics
"/>
Et ſimiliter vis plani
<
emph
type
="
italics
"/>
ef,
<
emph.end
type
="
italics
"/>
qua corpuſculum
<
emph
type
="
italics
"/>
P
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
</
subchap2
>
</
subchap1
>
</
chap
>
</
body
>
</
text
>
</
archimedes
>