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
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
<
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
="
039/01/254.jpg
"
pagenum
="
226
"/>
<
arrow.to.target
n
="
note202
"/>
una cum (1/A
<
emph
type
="
sup
"/>
<
emph
type
="
italics
"/>
n
<
emph.end
type
="
italics
"/>
<
emph.end
type
="
sup
"/>
) in
<
emph
type
="
italics
"/>
na
<
emph.end
type
="
italics
"/>
A
<
emph
type
="
sup
"/>
<
emph
type
="
italics
"/>
n
<
emph.end
type
="
italics
"/>
-1
<
emph.end
type
="
sup
"/>
erit nihil. </
s
>
<
s
>Et propterea momentum ip
<
lb
/>
ſius (1/A
<
emph
type
="
sup
"/>
<
emph
type
="
italics
"/>
n
<
emph.end
type
="
italics
"/>
<
emph.end
type
="
sup
"/>
) ſeu A
<
emph
type
="
sup
"/>
-
<
emph
type
="
italics
"/>
n
<
emph.end
type
="
italics
"/>
<
emph.end
type
="
sup
"/>
erit-(
<
emph
type
="
italics
"/>
na
<
emph.end
type
="
italics
"/>
/A
<
emph
type
="
sup
"/>
<
emph
type
="
italics
"/>
n
<
emph.end
type
="
italics
"/>
<
emph.end
type
="
sup
"/>
+1).
<
emph
type
="
italics
"/>
q.ED.
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
<
p
type
="
margin
">
<
s
>
<
margin.target
id
="
note202
"/>
DE MOTU
<
lb
/>
CORPORUM</
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
emph
type
="
italics
"/>
Cas.
<
emph.end
type
="
italics
"/>
5. Et cum A
<
emph
type
="
sup
"/>
1/2
<
emph.end
type
="
sup
"/>
in A
<
emph
type
="
sup
"/>
1/2
<
emph.end
type
="
sup
"/>
ſit A, momentum ipſius A
<
emph
type
="
sup
"/>
1/2
<
emph.end
type
="
sup
"/>
ductum in
<
lb
/>
2A
<
emph
type
="
sup
"/>
1/2
<
emph.end
type
="
sup
"/>
erit
<
emph
type
="
italics
"/>
a,
<
emph.end
type
="
italics
"/>
per Cas. </
s
>
<
s
>3: ideoque momentum ipſius A
<
emph
type
="
sup
"/>
1/2
<
emph.end
type
="
sup
"/>
erit (
<
emph
type
="
italics
"/>
a
<
emph.end
type
="
italics
"/>
/2A 1/2)
<
lb
/>
ſive 1/2
<
emph
type
="
italics
"/>
a
<
emph.end
type
="
italics
"/>
A
<
emph
type
="
sup
"/>
-1/2
<
emph.end
type
="
sup
"/>
. </
s
>
<
s
>Et generaliter ſi ponatur A
<
emph
type
="
sup
"/>
<
emph
type
="
italics
"/>
m/n
<
emph.end
type
="
italics
"/>
<
emph.end
type
="
sup
"/>
æquale B, erit A
<
emph
type
="
sup
"/>
<
emph
type
="
italics
"/>
m
<
emph.end
type
="
italics
"/>
<
emph.end
type
="
sup
"/>
æ
<
lb
/>
quale B
<
emph
type
="
sup
"/>
<
emph
type
="
italics
"/>
n
<
emph.end
type
="
italics
"/>
<
emph.end
type
="
sup
"/>
, ideoque
<
emph
type
="
italics
"/>
ma
<
emph.end
type
="
italics
"/>
A
<
emph
type
="
sup
"/>
<
emph
type
="
italics
"/>
m
<
emph.end
type
="
italics
"/>
-1
<
emph.end
type
="
sup
"/>
æquale
<
emph
type
="
italics
"/>
nb
<
emph.end
type
="
italics
"/>
B
<
emph
type
="
sup
"/>
<
emph
type
="
italics
"/>
n
<
emph.end
type
="
italics
"/>
-1,
<
emph.end
type
="
sup
"/>
&
<
emph
type
="
italics
"/>
ma
<
emph.end
type
="
italics
"/>
A
<
emph
type
="
sup
"/>
-1
<
emph.end
type
="
sup
"/>
æqua
<
lb
/>
le
<
emph
type
="
italics
"/>
nb
<
emph.end
type
="
italics
"/>
B
<
emph
type
="
sup
"/>
-1
<
emph.end
type
="
sup
"/>
ſeu
<
emph
type
="
italics
"/>
nb
<
emph.end
type
="
italics
"/>
A
<
emph
type
="
sup
"/>
-
<
emph
type
="
italics
"/>
m/n
<
emph.end
type
="
italics
"/>
<
emph.end
type
="
sup
"/>
, adeoque
<
emph
type
="
italics
"/>
m/n a
<
emph.end
type
="
italics
"/>
A
<
emph
type
="
sup
"/>
(
<
emph
type
="
italics
"/>
m-n/n
<
emph.end
type
="
italics
"/>
)
<
emph.end
type
="
sup
"/>
æquale
<
emph
type
="
italics
"/>
b,
<
emph.end
type
="
italics
"/>
id eſt, æquale
<
lb
/>
momento ipſius A
<
emph
type
="
sup
"/>
<
emph
type
="
italics
"/>
m/n
<
emph.end
type
="
italics
"/>
<
emph.end
type
="
sup
"/>
,
<
emph
type
="
italics
"/>
Q.E.D.
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
emph
type
="
italics
"/>
Cas.
<
emph.end
type
="
italics
"/>
6. Igitur Genitæ cujuſeunque A
<
emph
type
="
sup
"/>
<
emph
type
="
italics
"/>
m
<
emph.end
type
="
italics
"/>
<
emph.end
type
="
sup
"/>
B
<
emph
type
="
sup
"/>
<
emph
type
="
italics
"/>
n
<
emph.end
type
="
italics
"/>
<
emph.end
type
="
sup
"/>
momentum eſt mo
<
lb
/>
mentum ipſius A
<
emph
type
="
sup
"/>
<
emph
type
="
italics
"/>
m
<
emph.end
type
="
italics
"/>
<
emph.end
type
="
sup
"/>
ductum in B
<
emph
type
="
sup
"/>
<
emph
type
="
italics
"/>
n
<
emph.end
type
="
italics
"/>
<
emph.end
type
="
sup
"/>
, una cum momento ipſius B
<
emph
type
="
sup
"/>
<
emph
type
="
italics
"/>
n
<
emph.end
type
="
italics
"/>
<
emph.end
type
="
sup
"/>
du
<
lb
/>
cto in A
<
emph
type
="
sup
"/>
<
emph
type
="
italics
"/>
m
<
emph.end
type
="
italics
"/>
<
emph.end
type
="
sup
"/>
, id eſt
<
emph
type
="
italics
"/>
ma
<
emph.end
type
="
italics
"/>
A
<
emph
type
="
sup
"/>
<
emph
type
="
italics
"/>
m
<
emph.end
type
="
italics
"/>
-1
<
emph.end
type
="
sup
"/>
B
<
emph
type
="
sup
"/>
<
emph
type
="
italics
"/>
n
<
emph.end
type
="
italics
"/>
<
emph.end
type
="
sup
"/>
+
<
emph
type
="
italics
"/>
nb
<
emph.end
type
="
italics
"/>
B
<
emph
type
="
sup
"/>
<
emph
type
="
italics
"/>
n
<
emph.end
type
="
italics
"/>
-1
<
emph.end
type
="
sup
"/>
A
<
emph
type
="
sup
"/>
<
emph
type
="
italics
"/>
m
<
emph.end
type
="
italics
"/>
<
emph.end
type
="
sup
"/>
; idque ſive dignita
<
lb
/>
tum indices
<
emph
type
="
italics
"/>
m
<
emph.end
type
="
italics
"/>
&
<
emph
type
="
italics
"/>
n
<
emph.end
type
="
italics
"/>
ſint integri numeri vel fracti, ſive affirmati
<
lb
/>
vi vel negativi. </
s
>
<
s
>Et par eſt ratio contenti ſub pluribus dignitati
<
lb
/>
bus.
<
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. Hinc in continue proportionalibus, ſi terminus unus
<
lb
/>
datur, momenta terminorum reliquorum erunt ut iidem termini
<
lb
/>
multiplicati per numerum intervallorum inter ipſos & terminum
<
lb
/>
datum. </
s
>
<
s
>Sunto A, B, C, D, E, F continue proportionales; & ſi
<
lb
/>
detur terminus C, momenta reliquorum terminorum erunt inter
<
lb
/>
ſe ut-2A, -B, D, 2E, 3F. </
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
emph
type
="
italics
"/>
Corol.
<
emph.end
type
="
italics
"/>
2. Et ſi in quatuor proportionalibus duæ mediæ dentur,
<
lb
/>
momenta extremarum erunt ut eædem extremæ. </
s
>
<
s
>Idem intelligen
<
lb
/>
dum eſt de lateribus rectanguli cujuſcunQ.E.D.ti. </
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
emph
type
="
italics
"/>
Corol.
<
emph.end
type
="
italics
"/>
3. Et ſi ſumma vel differentia duorum quadratorum detur,
<
lb
/>
momenta laterum erunt reciproce ut latera. </
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
>In literis quæ mihi cum Geometra peritiſſimo
<
emph
type
="
italics
"/>
G.G. Leibnitio
<
emph.end
type
="
italics
"/>
an
<
lb
/>
nis abhinc decem intercedebant, cum ſignificarem me compotem
<
lb
/>
eſſe methodi determinandi Maximas & Minimas, ducendi Tangen
<
lb
/>
tes, & ſimilia peragendi, quæ in terminis ſurdis æque ac in ratio
<
lb
/>
nalibus procederet, & literis tranſpoſitis hanc ſententiam involven-</
s
>
</
p
>
</
subchap2
>
</
subchap1
>
</
chap
>
</
body
>
</
text
>
</
archimedes
>