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
>
271
272
273
274
275
276
277
278
279
280
<
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
>
<
pb
xlink:href
="
039/01/277.jpg
"
pagenum
="
249
"/>
<
p
type
="
main
">
<
s
>Nam velocitatis decrementum
<
emph
type
="
italics
"/>
PQ,
<
emph.end
type
="
italics
"/>
in data temporis particula
<
lb
/>
<
arrow.to.target
n
="
note225
"/>
factum, eſt ut ſumma reſiſtentiæ
<
emph
type
="
italics
"/>
APq
<
emph.end
type
="
italics
"/>
+2
<
emph
type
="
italics
"/>
BAP
<
emph.end
type
="
italics
"/>
& gravitatis
<
lb
/>
<
emph
type
="
italics
"/>
ABq-BDq,
<
emph.end
type
="
italics
"/>
id eſt, ut
<
emph
type
="
italics
"/>
BPq-BDq.
<
emph.end
type
="
italics
"/>
Eſt autem area
<
emph
type
="
italics
"/>
DTV
<
emph.end
type
="
italics
"/>
<
lb
/>
ad aream
<
emph
type
="
italics
"/>
DPQ
<
emph.end
type
="
italics
"/>
ut
<
emph
type
="
italics
"/>
DTq
<
emph.end
type
="
italics
"/>
ad
<
emph
type
="
italics
"/>
DPq
<
emph.end
type
="
italics
"/>
adeoque, ſi ad
<
emph
type
="
italics
"/>
DF
<
emph.end
type
="
italics
"/>
demitta
<
lb
/>
tur perpendiculum
<
emph
type
="
italics
"/>
GT,
<
emph.end
type
="
italics
"/>
ut
<
emph
type
="
italics
"/>
GTq
<
emph.end
type
="
italics
"/>
ſeu
<
emph
type
="
italics
"/>
GDq-DFq
<
emph.end
type
="
italics
"/>
ad
<
emph
type
="
italics
"/>
BDq
<
emph.end
type
="
italics
"/>
<
lb
/>
utque
<
emph
type
="
italics
"/>
GDq
<
emph.end
type
="
italics
"/>
ad
<
emph
type
="
italics
"/>
BPq
<
emph.end
type
="
italics
"/>
& diviſim ut
<
emph
type
="
italics
"/>
DFq
<
emph.end
type
="
italics
"/>
ad
<
emph
type
="
italics
"/>
BPq-BDq.
<
emph.end
type
="
italics
"/>
<
lb
/>
Quare cum area
<
emph
type
="
italics
"/>
DPQ
<
emph.end
type
="
italics
"/>
ſit ut
<
emph
type
="
italics
"/>
PQ,
<
emph.end
type
="
italics
"/>
id eſt, ut
<
emph
type
="
italics
"/>
BPq-BDq
<
emph.end
type
="
italics
"/>
; erit
<
lb
/>
area
<
emph
type
="
italics
"/>
DTV
<
emph.end
type
="
italics
"/>
ut datum
<
emph
type
="
italics
"/>
DFq.
<
emph.end
type
="
italics
"/>
Decreſcit igitur area
<
emph
type
="
italics
"/>
EDT
<
emph.end
type
="
italics
"/>
unifor
<
lb
/>
miter ſingulis temporis particulis æqualibus, per ſubductionem par
<
lb
/>
ticularum totidem datarum
<
emph
type
="
italics
"/>
DTV,
<
emph.end
type
="
italics
"/>
& propterea tempori propor
<
lb
/>
tionalis eſt.
<
emph
type
="
italics
"/>
Q.E.D.
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
<
p
type
="
margin
">
<
s
>
<
margin.target
id
="
note225
"/>
LIBER
<
lb
/>
SECUNDUS.</
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
emph
type
="
italics
"/>
Caſ.
<
emph.end
type
="
italics
"/>
3. Sit
<
emph
type
="
italics
"/>
AP
<
emph.end
type
="
italics
"/>
velocitas in deſcenſu corporis, &
<
emph
type
="
italics
"/>
APq+2BAP
<
emph.end
type
="
italics
"/>
<
lb
/>
reſiſtentia, &
<
emph
type
="
italics
"/>
BDq-ABq
<
emph.end
type
="
italics
"/>
vis gravitatis, exiſtente angulo
<
emph
type
="
italics
"/>
DBA
<
emph.end
type
="
italics
"/>
<
lb
/>
recto. </
s
>
<
s
>Et ſi centro
<
emph
type
="
italics
"/>
D,
<
emph.end
type
="
italics
"/>
vertice
<
lb
/>
<
figure
id
="
id.039.01.277.1.jpg
"
xlink:href
="
039/01/277/1.jpg
"
number
="
164
"/>
<
lb
/>
principali
<
emph
type
="
italics
"/>
B,
<
emph.end
type
="
italics
"/>
deſcribatur Hy
<
lb
/>
perbola rectangula
<
emph
type
="
italics
"/>
BETV
<
emph.end
type
="
italics
"/>
<
lb
/>
ſecans productas
<
emph
type
="
italics
"/>
DA, DP
<
emph.end
type
="
italics
"/>
&
<
lb
/>
<
emph
type
="
italics
"/>
DQ
<
emph.end
type
="
italics
"/>
in
<
emph
type
="
italics
"/>
E, T
<
emph.end
type
="
italics
"/>
&
<
emph
type
="
italics
"/>
V
<
emph.end
type
="
italics
"/>
; erit Hy
<
lb
/>
perbolæ hujus ſector
<
emph
type
="
italics
"/>
DET
<
emph.end
type
="
italics
"/>
ut
<
lb
/>
tempus deſcenſus. </
s
>
</
p
>
<
p
type
="
main
">
<
s
>Nam velocitatis
<
expan
abbr
="
incremẽtum
">incrementum</
expan
>
<
lb
/>
<
emph
type
="
italics
"/>
PQ,
<
emph.end
type
="
italics
"/>
eique proportionalis area
<
lb
/>
<
emph
type
="
italics
"/>
DPQ,
<
emph.end
type
="
italics
"/>
eſt ut exceſſus gravita
<
lb
/>
tis ſupra reſiſtentiam, id eſt, ut
<
lb
/>
<
emph
type
="
italics
"/>
BDq-ABq-2BAP-APq
<
emph.end
type
="
italics
"/>
<
lb
/>
ſeu
<
emph
type
="
italics
"/>
BDq-BPq.
<
emph.end
type
="
italics
"/>
Et area
<
lb
/>
<
emph
type
="
italics
"/>
DTV
<
emph.end
type
="
italics
"/>
eſt ad aream
<
emph
type
="
italics
"/>
DPQ
<
emph.end
type
="
italics
"/>
ut
<
lb
/>
<
emph
type
="
italics
"/>
DTq
<
emph.end
type
="
italics
"/>
ad
<
emph
type
="
italics
"/>
DPq,
<
emph.end
type
="
italics
"/>
adeoque ut
<
lb
/>
<
emph
type
="
italics
"/>
GTq
<
emph.end
type
="
italics
"/>
ſeu
<
emph
type
="
italics
"/>
GDq-BDq
<
emph.end
type
="
italics
"/>
ad
<
lb
/>
<
emph
type
="
italics
"/>
BPq
<
emph.end
type
="
italics
"/>
utque
<
emph
type
="
italics
"/>
GDq
<
emph.end
type
="
italics
"/>
ad
<
emph
type
="
italics
"/>
BDq
<
emph.end
type
="
italics
"/>
<
lb
/>
& diviſim ut
<
emph
type
="
italics
"/>
BDq
<
emph.end
type
="
italics
"/>
ad
<
emph
type
="
italics
"/>
BDq-BPq.
<
emph.end
type
="
italics
"/>
Quare cum area
<
emph
type
="
italics
"/>
DPQ
<
emph.end
type
="
italics
"/>
<
lb
/>
ſit ut
<
emph
type
="
italics
"/>
BDq-BPq,
<
emph.end
type
="
italics
"/>
erit area
<
emph
type
="
italics
"/>
DTV
<
emph.end
type
="
italics
"/>
ut datum
<
emph
type
="
italics
"/>
BDq.
<
emph.end
type
="
italics
"/>
Creſcit
<
lb
/>
igitur area
<
emph
type
="
italics
"/>
EDT
<
emph.end
type
="
italics
"/>
uniformiter ſingulis temporis particulis æquali
<
lb
/>
bus, per additionem totidem datarum particularum
<
emph
type
="
italics
"/>
DTV,
<
emph.end
type
="
italics
"/>
& prop
<
lb
/>
terea tempori deſcenſus proportionalis eſt.
<
emph
type
="
italics
"/>
Q.E.D.
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
emph
type
="
italics
"/>
Corol.
<
emph.end
type
="
italics
"/>
Igitur velocitas
<
emph
type
="
italics
"/>
AP
<
emph.end
type
="
italics
"/>
eſt ad velocitatem quam corpus tem
<
lb
/>
pore
<
emph
type
="
italics
"/>
EDT,
<
emph.end
type
="
italics
"/>
in ſpatio non reſiſtente, aſcendendo amittere vel de
<
lb
/>
ſcendendo acquirere poſſet, ut area trianguli
<
emph
type
="
italics
"/>
DAP
<
emph.end
type
="
italics
"/>
ad aream ſe
<
lb
/>
ctoris centro
<
emph
type
="
italics
"/>
D,
<
emph.end
type
="
italics
"/>
radio
<
emph
type
="
italics
"/>
DA,
<
emph.end
type
="
italics
"/>
angulo
<
emph
type
="
italics
"/>
ADT
<
emph.end
type
="
italics
"/>
deſcripti; ideoque ex
<
lb
/>
dato tempore datur. </
s
>
<
s
>Nam velocitas, in Medio non reſiſtente, tem-</
s
>
</
p
>
</
subchap2
>
</
subchap1
>
</
chap
>
</
body
>
</
text
>
</
archimedes
>