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
="
039/01/253.jpg
"
pagenum
="
225
"/>
dignitatum A
<
emph
type
="
sup
"/>
3
<
emph.end
type
="
sup
"/>
, A
<
emph
type
="
sup
"/>
3
<
emph.end
type
="
sup
"/>
, A
<
emph
type
="
sup
"/>
4
<
emph.end
type
="
sup
"/>
, A
<
emph
type
="
sup
"/>
1/2
<
emph.end
type
="
sup
"/>
, A
<
emph
type
="
sup
"/>
1/3
<
emph.end
type
="
sup
"/>
, A
<
emph
type
="
sup
"/>
1/3
<
emph.end
type
="
sup
"/>
, A
<
emph
type
="
sup
"/>
2/3
<
emph.end
type
="
sup
"/>
, A
<
emph
type
="
sup
"/>
-1
<
emph.end
type
="
sup
"/>
, A
<
emph
type
="
sup
"/>
-2
<
emph.end
type
="
sup
"/>
, & A
<
emph
type
="
sup
"/>
-1/2
<
emph.end
type
="
sup
"/>
momenta </
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
arrow.to.target
n
="
note201
"/>
2
<
emph
type
="
italics
"/>
a
<
emph.end
type
="
italics
"/>
A, 3
<
emph
type
="
italics
"/>
a
<
emph.end
type
="
italics
"/>
A
<
emph
type
="
sup
"/>
2
<
emph.end
type
="
sup
"/>
, 4
<
emph
type
="
italics
"/>
a
<
emph.end
type
="
italics
"/>
A
<
emph
type
="
sup
"/>
3
<
emph.end
type
="
sup
"/>
, 1/2
<
emph
type
="
italics
"/>
a
<
emph.end
type
="
italics
"/>
A
<
emph
type
="
sup
"/>
-1/2
<
emph.end
type
="
sup
"/>
, 3/2
<
emph
type
="
italics
"/>
a
<
emph.end
type
="
italics
"/>
A
<
emph
type
="
sup
"/>
1/2
<
emph.end
type
="
sup
"/>
, 1/3
<
emph
type
="
italics
"/>
a
<
emph.end
type
="
italics
"/>
A
<
emph
type
="
sup
"/>
-2/3
<
emph.end
type
="
sup
"/>
, 2/3
<
emph
type
="
italics
"/>
a
<
emph.end
type
="
italics
"/>
A
<
emph
type
="
sup
"/>
-1/3
<
emph.end
type
="
sup
"/>
, -
<
emph
type
="
italics
"/>
a
<
emph.end
type
="
italics
"/>
A
<
emph
type
="
sup
"/>
-2
<
emph.end
type
="
sup
"/>
,
<
lb
/>
-2
<
emph
type
="
italics
"/>
a
<
emph.end
type
="
italics
"/>
A
<
emph
type
="
sup
"/>
-3
<
emph.end
type
="
sup
"/>
, & -1/2
<
emph
type
="
italics
"/>
a
<
emph.end
type
="
italics
"/>
A
<
emph
type
="
sup
"/>
-1/2
<
emph.end
type
="
sup
"/>
reſpective. </
s
>
<
s
>Et generaliter, ut dignitatis
<
lb
/>
cujuſcunque A
<
emph
type
="
sup
"/>
<
emph
type
="
italics
"/>
n/m
<
emph.end
type
="
italics
"/>
<
emph.end
type
="
sup
"/>
momentum fuerit
<
emph
type
="
italics
"/>
n/m a
<
emph.end
type
="
italics
"/>
A
<
emph
type
="
sup
"/>
(
<
emph
type
="
italics
"/>
n-m/m
<
emph.end
type
="
italics
"/>
)
<
emph.end
type
="
sup
"/>
. </
s
>
<
s
>Item ut Genitæ
<
lb
/>
A
<
emph
type
="
sup
"/>
2
<
emph.end
type
="
sup
"/>
B momentum fuerit 2
<
emph
type
="
italics
"/>
a
<
emph.end
type
="
italics
"/>
AB+
<
emph
type
="
italics
"/>
b
<
emph.end
type
="
italics
"/>
A
<
emph
type
="
sup
"/>
2
<
emph.end
type
="
sup
"/>
; & Genitæ A
<
emph
type
="
sup
"/>
3
<
emph.end
type
="
sup
"/>
B
<
emph
type
="
sup
"/>
4
<
emph.end
type
="
sup
"/>
C
<
emph
type
="
sup
"/>
2
<
emph.end
type
="
sup
"/>
momen
<
lb
/>
tum 3
<
emph
type
="
italics
"/>
a
<
emph.end
type
="
italics
"/>
A
<
emph
type
="
sup
"/>
2
<
emph.end
type
="
sup
"/>
B
<
emph
type
="
sup
"/>
4
<
emph.end
type
="
sup
"/>
C
<
emph
type
="
sup
"/>
2
<
emph.end
type
="
sup
"/>
+4
<
emph
type
="
italics
"/>
b
<
emph.end
type
="
italics
"/>
A
<
emph
type
="
sup
"/>
3
<
emph.end
type
="
sup
"/>
B
<
emph
type
="
sup
"/>
3
<
emph.end
type
="
sup
"/>
C
<
emph
type
="
sup
"/>
2
<
emph.end
type
="
sup
"/>
+2
<
emph
type
="
italics
"/>
c
<
emph.end
type
="
italics
"/>
A
<
emph
type
="
sup
"/>
3
<
emph.end
type
="
sup
"/>
B
<
emph
type
="
sup
"/>
4
<
emph.end
type
="
sup
"/>
C; & Genitæ (A
<
emph
type
="
sup
"/>
3
<
emph.end
type
="
sup
"/>
/B
<
emph
type
="
sup
"/>
2
<
emph.end
type
="
sup
"/>
) ſi
<
lb
/>
ve A
<
emph
type
="
sup
"/>
3
<
emph.end
type
="
sup
"/>
B
<
emph
type
="
sup
"/>
-2
<
emph.end
type
="
sup
"/>
momentum 3
<
emph
type
="
italics
"/>
a
<
emph.end
type
="
italics
"/>
A
<
emph
type
="
sup
"/>
2
<
emph.end
type
="
sup
"/>
B
<
emph
type
="
sup
"/>
-2
<
emph.end
type
="
sup
"/>
-2
<
emph
type
="
italics
"/>
b
<
emph.end
type
="
italics
"/>
A
<
emph
type
="
sup
"/>
3
<
emph.end
type
="
sup
"/>
B
<
emph
type
="
sup
"/>
-3
<
emph.end
type
="
sup
"/>
: & ſic in cæteris. </
s
>
<
s
>
<
lb
/>
Demonſtratur vero Lemma in hunc modum. </
s
>
</
p
>
<
p
type
="
margin
">
<
s
>
<
margin.target
id
="
note201
"/>
LIBER
<
lb
/>
SECUNDUS.</
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
emph
type
="
italics
"/>
Cas.
<
emph.end
type
="
italics
"/>
1. Rectangulum quodvis motu perpetuo auctum AB,
<
lb
/>
ubi de lateribus A & B deerant momentorum dimidia 1/2
<
emph
type
="
italics
"/>
a
<
emph.end
type
="
italics
"/>
& 1/2
<
emph
type
="
italics
"/>
b,
<
emph.end
type
="
italics
"/>
<
lb
/>
fuit A-1/2
<
emph
type
="
italics
"/>
a
<
emph.end
type
="
italics
"/>
in B-1/2
<
emph
type
="
italics
"/>
b,
<
emph.end
type
="
italics
"/>
ſeu AB-1/2
<
emph
type
="
italics
"/>
a
<
emph.end
type
="
italics
"/>
B-1/2
<
emph
type
="
italics
"/>
b
<
emph.end
type
="
italics
"/>
A+1/4
<
emph
type
="
italics
"/>
ab
<
emph.end
type
="
italics
"/>
; & quam pri
<
lb
/>
mum latera A & B alteris momentorum dimidiis aucta ſunt, eva
<
lb
/>
dit A+1/2
<
emph
type
="
italics
"/>
a
<
emph.end
type
="
italics
"/>
in B+1/2
<
emph
type
="
italics
"/>
b
<
emph.end
type
="
italics
"/>
ſeu AB+1/2
<
emph
type
="
italics
"/>
a
<
emph.end
type
="
italics
"/>
B+1/2
<
emph
type
="
italics
"/>
b
<
emph.end
type
="
italics
"/>
A+1/4
<
emph
type
="
italics
"/>
ab.
<
emph.end
type
="
italics
"/>
De hoc rectan
<
lb
/>
gulo ſubducatur rectangulum prius, & manebit exceſſus
<
emph
type
="
italics
"/>
a
<
emph.end
type
="
italics
"/>
B+
<
emph
type
="
italics
"/>
b
<
emph.end
type
="
italics
"/>
A. </
s
>
<
s
>
<
lb
/>
Igitur laterum incrementis totis
<
emph
type
="
italics
"/>
a
<
emph.end
type
="
italics
"/>
&
<
emph
type
="
italics
"/>
b
<
emph.end
type
="
italics
"/>
generatur rectanguli incre
<
lb
/>
mentum
<
emph
type
="
italics
"/>
a
<
emph.end
type
="
italics
"/>
B+
<
emph
type
="
italics
"/>
b
<
emph.end
type
="
italics
"/>
A.
<
emph
type
="
italics
"/>
Q.E.D.
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
emph
type
="
italics
"/>
Cas.
<
emph.end
type
="
italics
"/>
2. Ponatur AB ſemper æquale G, & contenti ABC ſeu
<
lb
/>
GC momentum (per Cas. </
s
>
<
s
>1.) erit
<
emph
type
="
italics
"/>
g
<
emph.end
type
="
italics
"/>
C+
<
emph
type
="
italics
"/>
c
<
emph.end
type
="
italics
"/>
G, id eſt (ſi pro G &
<
emph
type
="
italics
"/>
g
<
emph.end
type
="
italics
"/>
<
lb
/>
ſcribantur AB &
<
emph
type
="
italics
"/>
a
<
emph.end
type
="
italics
"/>
B+
<
emph
type
="
italics
"/>
b
<
emph.end
type
="
italics
"/>
A)
<
emph
type
="
italics
"/>
a
<
emph.end
type
="
italics
"/>
BC+
<
emph
type
="
italics
"/>
b
<
emph.end
type
="
italics
"/>
AC+
<
emph
type
="
italics
"/>
c
<
emph.end
type
="
italics
"/>
AB. </
s
>
<
s
>Et par eſt ra
<
lb
/>
tio contenti ſub lateribus quotcunque.
<
emph
type
="
italics
"/>
Q.E.D.
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
emph
type
="
italics
"/>
Cas.
<
emph.end
type
="
italics
"/>
3. Ponantur latera A, B, C ſibi mutuo ſemper æqualia; &
<
lb
/>
ipſius A
<
emph
type
="
sup
"/>
2
<
emph.end
type
="
sup
"/>
, id eſt rectanguli AB, momentum
<
emph
type
="
italics
"/>
a
<
emph.end
type
="
italics
"/>
B+
<
emph
type
="
italics
"/>
b
<
emph.end
type
="
italics
"/>
A erit 2
<
emph
type
="
italics
"/>
a
<
emph.end
type
="
italics
"/>
A, ip
<
lb
/>
ſius autem A
<
emph
type
="
sup
"/>
3
<
emph.end
type
="
sup
"/>
, id eſt contenti ABC, momentum
<
emph
type
="
italics
"/>
a
<
emph.end
type
="
italics
"/>
BC+
<
emph
type
="
italics
"/>
b
<
emph.end
type
="
italics
"/>
AC
<
lb
/>
+
<
emph
type
="
italics
"/>
c
<
emph.end
type
="
italics
"/>
AB erit 3
<
emph
type
="
italics
"/>
a
<
emph.end
type
="
italics
"/>
A
<
emph
type
="
sup
"/>
2
<
emph.end
type
="
sup
"/>
. </
s
>
<
s
>Et eodem argumento momentum dignitatis
<
lb
/>
cujuſcunque A
<
emph
type
="
sup
"/>
<
emph
type
="
italics
"/>
n
<
emph.end
type
="
italics
"/>
<
emph.end
type
="
sup
"/>
eſt
<
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
"/>
<
emph
type
="
italics
"/>
Q.E.D.
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
emph
type
="
italics
"/>
Cas.
<
emph.end
type
="
italics
"/>
4. Unde cum 1/A in A ſit 1, momentum ipſius 1/A ductum
<
lb
/>
in A, una cum 1/A ducto in
<
emph
type
="
italics
"/>
a
<
emph.end
type
="
italics
"/>
erit momentum ipſius 1, id eſt, NI
<
lb
/>
hil. </
s
>
<
s
>Proinde momentum ipſius 1/A ſeu ipſius A
<
emph
type
="
sup
"/>
-1
<
emph.end
type
="
sup
"/>
eſt (-
<
emph
type
="
italics
"/>
a
<
emph.end
type
="
italics
"/>
/A
<
emph
type
="
sup
"/>
2
<
emph.end
type
="
sup
"/>
). Et ge
<
lb
/>
neraliter cum (1/A
<
emph
type
="
sup
"/>
<
emph
type
="
italics
"/>
n
<
emph.end
type
="
italics
"/>
<
emph.end
type
="
sup
"/>
) in A
<
emph
type
="
sup
"/>
<
emph
type
="
italics
"/>
n
<
emph.end
type
="
italics
"/>
<
emph.end
type
="
sup
"/>
ſit 1, momentum ipſius (1/A
<
emph
type
="
sup
"/>
<
emph
type
="
italics
"/>
n
<
emph.end
type
="
italics
"/>
<
emph.end
type
="
sup
"/>
) ductum in A
<
emph
type
="
sup
"/>
<
emph
type
="
italics
"/>
n
<
emph.end
type
="
italics
"/>
<
emph.end
type
="
sup
"/>
</
s
>
</
p
>
</
subchap2
>
</
subchap1
>
</
chap
>
</
body
>
</
text
>
</
archimedes
>