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
>
121
122
123
124
125
126
127
128
129
130
<
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
="
039/01/125.jpg
"
pagenum
="
97
"/>
<
arrow.to.target
n
="
note73
"/>
</
s
>
</
p
>
</
subchap2
>
<
subchap2
>
<
p
type
="
margin
">
<
s
>
<
margin.target
id
="
note73
"/>
LIBER
<
lb
/>
PRIMUS.</
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
emph
type
="
center
"/>
SECTIO VI.
<
emph.end
type
="
center
"/>
</
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
emph
type
="
center
"/>
<
emph
type
="
italics
"/>
De Inventione Motuum in Orbibus datis.
<
emph.end
type
="
italics
"/>
<
emph.end
type
="
center
"/>
</
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
emph
type
="
center
"/>
PROPOSITIO XXX. PROBLEMA XXII.
<
emph.end
type
="
center
"/>
</
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
emph
type
="
center
"/>
<
emph
type
="
italics
"/>
Corporis in data Trajectoria Parabolica moti invenire locum ad
<
lb
/>
tempus aſſignatum.
<
emph.end
type
="
italics
"/>
<
emph.end
type
="
center
"/>
</
s
>
</
p
>
<
p
type
="
main
">
<
s
>Sit
<
emph
type
="
italics
"/>
S
<
emph.end
type
="
italics
"/>
umbilicus &
<
emph
type
="
italics
"/>
A
<
emph.end
type
="
italics
"/>
vertex principa
<
lb
/>
<
figure
id
="
id.039.01.125.1.jpg
"
xlink:href
="
039/01/125/1.jpg
"
number
="
73
"/>
<
lb
/>
lis Parabolæ, ſitque 4
<
emph
type
="
italics
"/>
ASXM
<
emph.end
type
="
italics
"/>
æquale
<
lb
/>
areæ Parabolicæ abſcindendæ
<
emph
type
="
italics
"/>
APS,
<
emph.end
type
="
italics
"/>
<
lb
/>
quæ radio
<
emph
type
="
italics
"/>
SP,
<
emph.end
type
="
italics
"/>
vel poſt exceſſum cor
<
lb
/>
poris de vertice deſcripta fuit, vel an
<
lb
/>
te appulſum ejus ad verticem deſcri
<
lb
/>
benda eſt. </
s
>
<
s
>Innoteſcit quantitas areæ il
<
lb
/>
lius abſcindendæ ex tempore ipſi pro
<
lb
/>
portionali. </
s
>
<
s
>Biſeca
<
emph
type
="
italics
"/>
AS
<
emph.end
type
="
italics
"/>
in
<
emph
type
="
italics
"/>
G,
<
emph.end
type
="
italics
"/>
erigeque
<
lb
/>
perpendiculum
<
emph
type
="
italics
"/>
GH
<
emph.end
type
="
italics
"/>
æquale 3 M, &
<
lb
/>
Circulus centro
<
emph
type
="
italics
"/>
H,
<
emph.end
type
="
italics
"/>
intervallo
<
emph
type
="
italics
"/>
HS
<
emph.end
type
="
italics
"/>
<
lb
/>
deſcriptus ſecabit Parabolam in loco
<
lb
/>
quæſito
<
emph
type
="
italics
"/>
P.
<
emph.end
type
="
italics
"/>
Nam, demiſſa ad axem
<
lb
/>
perpendiculari
<
emph
type
="
italics
"/>
PO
<
emph.end
type
="
italics
"/>
& ducta
<
emph
type
="
italics
"/>
PH,
<
emph.end
type
="
italics
"/>
eſt
<
lb
/>
<
emph
type
="
italics
"/>
AGq+GHq (=HP q=—AO-AG: quad.+—PO-GH: quad.)=
<
lb
/>
AOq+POq-2
<
expan
abbr
="
GAO-2GHXPO+AGq+GHq.
">GAO-2GHXPO+AGq+GHque</
expan
>
<
emph.end
type
="
italics
"/>
Unde
<
lb
/>
2
<
emph
type
="
italics
"/>
GHXPO (=AOq+POq-2GAO)=AOq+1/4
<
expan
abbr
="
POq.
">POque</
expan
>
<
emph.end
type
="
italics
"/>
<
lb
/>
Pro
<
emph
type
="
italics
"/>
AOq
<
emph.end
type
="
italics
"/>
ſcribe (
<
emph
type
="
italics
"/>
AOXPOq/4AS
<
emph.end
type
="
italics
"/>
); &, applicatis terminis omnibus ad
<
lb
/>
3
<
emph
type
="
italics
"/>
PO
<
emph.end
type
="
italics
"/>
ductiſQ.E.I. 2
<
emph
type
="
italics
"/>
AS,
<
emph.end
type
="
italics
"/>
fiet 4/3
<
emph
type
="
italics
"/>
GHXAS(=1/6AOXPO+1/2 ASXPO
<
lb
/>
=(AO+3AS/6)XPO=(4AO-3SO/6)XPO
<
emph.end
type
="
italics
"/>
=areæ —
<
emph
type
="
italics
"/>
APO-SPO)
<
emph.end
type
="
italics
"/>
<
lb
/>
=areæ
<
emph
type
="
italics
"/>
APS.
<
emph.end
type
="
italics
"/>
Sed
<
emph
type
="
italics
"/>
GH
<
emph.end
type
="
italics
"/>
erat 3 M, & inde 4/3
<
emph
type
="
italics
"/>
GHXAS
<
emph.end
type
="
italics
"/>
eſt 4
<
emph
type
="
italics
"/>
AS
<
emph.end
type
="
italics
"/>
XM. </
s
>
<
s
>
<
lb
/>
Ergo area abſciſſa
<
emph
type
="
italics
"/>
APS
<
emph.end
type
="
italics
"/>
æqualis eſt abſcindendæ 4
<
emph
type
="
italics
"/>
ASXM. Q.E.D.
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
emph
type
="
italics
"/>
Corol.
<
emph.end
type
="
italics
"/>
1. Hinc
<
emph
type
="
italics
"/>
GH
<
emph.end
type
="
italics
"/>
eſt ad
<
emph
type
="
italics
"/>
AS,
<
emph.end
type
="
italics
"/>
ut tempus quo corpùs deſcrip
<
lb
/>
ſit arcum
<
emph
type
="
italics
"/>
AP
<
emph.end
type
="
italics
"/>
ad tempus quo corpus deſcripſit arcum inter verti
<
lb
/>
cem
<
emph
type
="
italics
"/>
A
<
emph.end
type
="
italics
"/>
& perpendiculum ad axem ab umbilico
<
emph
type
="
italics
"/>
S
<
emph.end
type
="
italics
"/>
erectum. </
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
emph
type
="
italics
"/>
Corol.
<
emph.end
type
="
italics
"/>
2. Et Circulo
<
emph
type
="
italics
"/>
ASP
<
emph.end
type
="
italics
"/>
per corpus motum
<
emph
type
="
italics
"/>
P
<
emph.end
type
="
italics
"/>
perpetuo tranſ
<
lb
/>
eunte, velocitas puncti
<
emph
type
="
italics
"/>
H
<
emph.end
type
="
italics
"/>
eſt ad velocitatem quam corpus habuit </
s
>
</
p
>
</
subchap2
>
</
subchap1
>
</
chap
>
</
body
>
</
text
>
</
archimedes
>