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
>
61
62
63
64
65
66
67
68
69
70
<
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
="
039/01/066.jpg
"
pagenum
="
38
"/>
<
arrow.to.target
n
="
note18
"/>
corpus alterum
<
emph
type
="
italics
"/>
T,
<
emph.end
type
="
italics
"/>
erunt areæ illæ temporibus quamproxime pro
<
lb
/>
portionales. </
s
>
</
p
>
<
p
type
="
margin
">
<
s
>
<
margin.target
id
="
note18
"/>
DE MOTU
<
lb
/>
CORPORUM</
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
emph
type
="
italics
"/>
Corol.
<
emph.end
type
="
italics
"/>
4. Si corpus
<
emph
type
="
italics
"/>
L
<
emph.end
type
="
italics
"/>
radio ad alterum corpus
<
emph
type
="
italics
"/>
T
<
emph.end
type
="
italics
"/>
ducto deſcri
<
lb
/>
bit areas quæ, cum temporibus collatæ, ſunt valde inæquales; &
<
lb
/>
corpus illud alterum
<
emph
type
="
italics
"/>
T
<
emph.end
type
="
italics
"/>
vel quieſcit vel movetur uniformiter in di
<
lb
/>
rectum: actio vis centripetæ ad corpus illud alterum
<
emph
type
="
italics
"/>
T
<
emph.end
type
="
italics
"/>
tendentis,
<
lb
/>
vel nulla eſt, vel miſcetur & componitur cum actionibus admodum
<
lb
/>
potentibus aliarum virium: Viſque tota ex omnibus, ſi plures ſunt
<
lb
/>
vires, compoſita, ad aliud (ſive immobile ſive mobile) centrum
<
lb
/>
dirigitur. </
s
>
<
s
>Idem obtinet, ubi corpus alterum motu quocunque mo
<
lb
/>
vetur; ſi modo vis centripeta ſumatur, quæ reſtat poſt ſubductio
<
lb
/>
nem vis totius in corpus illud alterum
<
emph
type
="
italics
"/>
T
<
emph.end
type
="
italics
"/>
agentis. </
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
emph
type
="
center
"/>
<
emph
type
="
italics
"/>
Scholium.
<
emph.end
type
="
italics
"/>
<
emph.end
type
="
center
"/>
</
s
>
</
p
>
<
p
type
="
main
">
<
s
>Quoniam æquabilis arearum deſcriptio Index eſt Centri, quod
<
lb
/>
vis illa reſpicit qua corpus maxime afficitur, quaque retrahitur a mo
<
lb
/>
tu rectilineo & in orbita ſua retinetur: quidni uſurpemus in ſequen
<
lb
/>
tibus æquabilem arearum deſcriptionem, ut Indicem Centri circum
<
lb
/>
quod motus omnis circularis in ſpatiis liberis peragitur? </
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
emph
type
="
center
"/>
PROPOSITIO IV. THEOREMA IV.
<
emph.end
type
="
center
"/>
</
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
emph
type
="
italics
"/>
Corporum, quæ diverſos circulos æquabili motu deſcribunt, vires cen
<
lb
/>
tripetas ad centra eorundem circulorum tendere; & eſſe inter ſe,
<
lb
/>
ut ſunt arcuum ſimul deſcriptorum quadrata applicata ad circulo
<
lb
/>
rum radios.
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
<
p
type
="
main
">
<
s
>Tendunt hæ vires ad centra circulorum per Prop.II. & Corol. </
s
>
<
s
>II.
<
lb
/>
Prop. </
s
>
<
s
>1; & ſunt inter ſe ut arcuum æqualibus temporibus quam miNI
<
lb
/>
mis deſcriptorum ſinus verſi per Corol. </
s
>
<
s
>IV. Prop. </
s
>
<
s
>I; hoc eſt, ut qua
<
lb
/>
drata arcuum eorundem ad diametros circulorum applicata per
<
lb
/>
Lem. </
s
>
<
s
>VII: & propterea, cum hi arcus ſint ut arcus temporibus
<
lb
/>
quibuſvis æqualibus deſcripti, & diametri ſint ut eorum radii; vi
<
lb
/>
res erunt ut arcuum quorumvis ſimul deſcriptorum quadrata ap
<
lb
/>
plicata ad radios circulorum.
<
emph
type
="
italics
"/>
Q.E.D.
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
emph
type
="
italics
"/>
Corol.
<
emph.end
type
="
italics
"/>
1. Igitur, cum arcus illi ſint ut velocitates corporum, vi
<
lb
/>
res centripetæ ſunt ut velocitatum quadrata applicata ad radios
<
lb
/>
circulorum: hoc eſt, ut cum Geometris loquar, vires ſunt in ra
<
lb
/>
tione compoſita ex duplicata ratione velocitatum directe & ratione
<
lb
/>
ſimplici radiorum inverſe. </
s
>
</
p
>
</
subchap2
>
</
subchap1
>
</
chap
>
</
body
>
</
text
>
</
archimedes
>