Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
Text
Text Image
Image
XML
Thumbnail overview
Document information
None
Concordance
Figures
Thumbnails
page
|<
<
of 524
>
>|
<
archimedes
>
<
text
>
<
body
>
<
chap
>
<
subchap1
>
<
subchap2
>
<
p
type
="
main
">
<
s
>
<
pb
xlink:href
="
039/01/259.jpg
"
pagenum
="
231
"/>
<
emph
type
="
italics
"/>
PQ
<
emph.end
type
="
italics
"/>
generantur, ut ſumma particularum ſectoris
<
emph
type
="
italics
"/>
ATD,
<
emph.end
type
="
italics
"/>
id eſt, </
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
arrow.to.target
n
="
note207
"/>
tempus totum ut ſector totus.
<
emph
type
="
italics
"/>
Q.E.D.
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
<
p
type
="
margin
">
<
s
>
<
margin.target
id
="
note207
"/>
LIBER
<
lb
/>
SECUNDUS.</
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
emph
type
="
italics
"/>
Corol.
<
emph.end
type
="
italics
"/>
1. Hinc ſi
<
emph
type
="
italics
"/>
AB
<
emph.end
type
="
italics
"/>
æquetur quartæ parti ipſius
<
emph
type
="
italics
"/>
AC,
<
emph.end
type
="
italics
"/>
ſpatium
<
lb
/>
quod corpus tempore quovis cadendo deſcribit, erit ad ſpatium
<
lb
/>
quod corpus velocitate maxima
<
emph
type
="
italics
"/>
AC,
<
emph.end
type
="
italics
"/>
eodem tempore uniformiter
<
lb
/>
progrediendo deſcribere poteſt, ut area
<
emph
type
="
italics
"/>
ABNK,
<
emph.end
type
="
italics
"/>
qua ſpatium
<
lb
/>
cadendo deſcriptum exponitur, ad aream
<
emph
type
="
italics
"/>
ATD
<
emph.end
type
="
italics
"/>
qua tempus ex
<
lb
/>
ponitur. </
s
>
<
s
>Nam cum ſit
<
emph
type
="
italics
"/>
AC
<
emph.end
type
="
italics
"/>
ad
<
emph
type
="
italics
"/>
AP
<
emph.end
type
="
italics
"/>
ut
<
emph
type
="
italics
"/>
AP
<
emph.end
type
="
italics
"/>
ad
<
emph
type
="
italics
"/>
AK,
<
emph.end
type
="
italics
"/>
erit (per
<
lb
/>
Corol. </
s
>
<
s
>1, Lem. </
s
>
<
s
>11 hujus)
<
emph
type
="
italics
"/>
LK
<
emph.end
type
="
italics
"/>
ad
<
emph
type
="
italics
"/>
PQ
<
emph.end
type
="
italics
"/>
ut 2
<
emph
type
="
italics
"/>
AK
<
emph.end
type
="
italics
"/>
ad
<
emph
type
="
italics
"/>
AP,
<
emph.end
type
="
italics
"/>
hoc eſt,
<
lb
/>
ut 2
<
emph
type
="
italics
"/>
AP
<
emph.end
type
="
italics
"/>
ad
<
emph
type
="
italics
"/>
AC,
<
emph.end
type
="
italics
"/>
& inde
<
emph
type
="
italics
"/>
LK
<
emph.end
type
="
italics
"/>
ad 1/2
<
emph
type
="
italics
"/>
PQ
<
emph.end
type
="
italics
"/>
ut
<
emph
type
="
italics
"/>
AP
<
emph.end
type
="
italics
"/>
ad (1/4
<
emph
type
="
italics
"/>
AC
<
emph.end
type
="
italics
"/>
vel)
<
lb
/>
<
emph
type
="
italics
"/>
AB
<
emph.end
type
="
italics
"/>
; eſt &
<
emph
type
="
italics
"/>
KN
<
emph.end
type
="
italics
"/>
ad (
<
emph
type
="
italics
"/>
AC
<
emph.end
type
="
italics
"/>
vel)
<
emph
type
="
italics
"/>
AD
<
emph.end
type
="
italics
"/>
ut
<
emph
type
="
italics
"/>
AB
<
emph.end
type
="
italics
"/>
ad
<
emph
type
="
italics
"/>
CK
<
emph.end
type
="
italics
"/>
; itaque ex
<
lb
/>
æquo
<
emph
type
="
italics
"/>
LKN
<
emph.end
type
="
italics
"/>
ad
<
emph
type
="
italics
"/>
DPQ
<
emph.end
type
="
italics
"/>
ut
<
emph
type
="
italics
"/>
AP
<
emph.end
type
="
italics
"/>
ad
<
emph
type
="
italics
"/>
CK.
<
emph.end
type
="
italics
"/>
Sed erat
<
emph
type
="
italics
"/>
DPQ
<
emph.end
type
="
italics
"/>
ad
<
lb
/>
<
emph
type
="
italics
"/>
DTV
<
emph.end
type
="
italics
"/>
ut
<
emph
type
="
italics
"/>
CK
<
emph.end
type
="
italics
"/>
ad
<
emph
type
="
italics
"/>
AC.
<
emph.end
type
="
italics
"/>
Ergo rurſus ex æquo
<
emph
type
="
italics
"/>
LKN
<
emph.end
type
="
italics
"/>
eſt ad
<
emph
type
="
italics
"/>
DTV
<
emph.end
type
="
italics
"/>
<
lb
/>
ut
<
emph
type
="
italics
"/>
AP
<
emph.end
type
="
italics
"/>
ad
<
emph
type
="
italics
"/>
AC
<
emph.end
type
="
italics
"/>
; hoc eſt, ut velocitas corporis cadentis ad veloci
<
lb
/>
tatem maximam quam corpus cadendo poteſt acquirere. </
s
>
<
s
>Cum
<
lb
/>
igitur arearum
<
emph
type
="
italics
"/>
ABNK
<
emph.end
type
="
italics
"/>
&
<
emph
type
="
italics
"/>
ATD
<
emph.end
type
="
italics
"/>
momenta
<
emph
type
="
italics
"/>
LKN
<
emph.end
type
="
italics
"/>
&
<
emph
type
="
italics
"/>
DTV
<
emph.end
type
="
italics
"/>
<
lb
/>
ſunt ut velocitates, erunt arearum illarum partes omnes ſimul
<
lb
/>
genitæ ut ſpatia ſimul deſcripta, ideoque areæ totæ ab initio
<
lb
/>
genitæ
<
emph
type
="
italics
"/>
ABNK
<
emph.end
type
="
italics
"/>
&
<
emph
type
="
italics
"/>
ATD
<
emph.end
type
="
italics
"/>
ut ſpatia tota ab initio deſcenſus de
<
lb
/>
ſcripta.
<
emph
type
="
italics
"/>
Q.E.D.
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
emph
type
="
italics
"/>
Corol.
<
emph.end
type
="
italics
"/>
2. Idem conſequitur etiam de ſpatio quod in aſcenſu de
<
lb
/>
ſcribitur. </
s
>
<
s
>Nimirum quod ſpatium illud omne ſit ad ſpatium, uNI
<
lb
/>
formi cum velocitate
<
emph
type
="
italics
"/>
AC
<
emph.end
type
="
italics
"/>
eodem tempore deſcriptum, ut eſt area
<
lb
/>
<
emph
type
="
italics
"/>
ABnk
<
emph.end
type
="
italics
"/>
ad ſectorem
<
emph
type
="
italics
"/>
ADt.
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
emph
type
="
italics
"/>
Corol.
<
emph.end
type
="
italics
"/>
3. Velocitas corporis tempore
<
emph
type
="
italics
"/>
ATD
<
emph.end
type
="
italics
"/>
cadentis eſt ad ve
<
lb
/>
locitatem, quam eodem tempore in ſpatio non reſiſtente acquire
<
lb
/>
ret, ut triangulum
<
emph
type
="
italics
"/>
APD
<
emph.end
type
="
italics
"/>
ad ſectorem Hyperbolicum
<
emph
type
="
italics
"/>
ATD.
<
emph.end
type
="
italics
"/>
<
lb
/>
Nam velocitas in Medio non reſiſtente foret ut tempus
<
emph
type
="
italics
"/>
ATD,
<
emph.end
type
="
italics
"/>
&
<
lb
/>
in Medio reſiſtente eſt ut
<
emph
type
="
italics
"/>
AP,
<
emph.end
type
="
italics
"/>
id eſt, ut triangulum
<
emph
type
="
italics
"/>
APD.
<
emph.end
type
="
italics
"/>
Et
<
lb
/>
velocitates illæ initio deſcenſus æquantur inter ſe, perinde ut areæ
<
lb
/>
illæ
<
emph
type
="
italics
"/>
ATD, APD.
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
emph
type
="
italics
"/>
Corol.
<
emph.end
type
="
italics
"/>
4. Eodem argumento velocitas in aſcenſu eſt ad velocita
<
lb
/>
tem, qua corpus eodem tempore in ſpatio non reſiſtente omnem
<
lb
/>
ſuum aſcendendi motum amittere poſſet, ut triangulum
<
emph
type
="
italics
"/>
ApD
<
emph.end
type
="
italics
"/>
ad
<
lb
/>
ſectorem Circularem
<
emph
type
="
italics
"/>
AtD
<
emph.end
type
="
italics
"/>
; ſive ut recta
<
emph
type
="
italics
"/>
Ap
<
emph.end
type
="
italics
"/>
ad arcum
<
emph
type
="
italics
"/>
At.
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
emph
type
="
italics
"/>
Corol.
<
emph.end
type
="
italics
"/>
5. Eſt igitur tempus quo corpus in Medio reſiſtente caden
<
lb
/>
do velocitatem
<
emph
type
="
italics
"/>
AP
<
emph.end
type
="
italics
"/>
acquirit, ad tempus quo velocitatem maximam
<
lb
/>
<
emph
type
="
italics
"/>
AC
<
emph.end
type
="
italics
"/>
in ſpatio non reſiſtente cadendo acquirere poſſet, ut ſector
<
lb
/>
<
emph
type
="
italics
"/>
ADT
<
emph.end
type
="
italics
"/>
ad triangulum
<
emph
type
="
italics
"/>
ADC
<
emph.end
type
="
italics
"/>
: & tempus, quo velocitatem
<
emph
type
="
italics
"/>
Ap
<
emph.end
type
="
italics
"/>
in </
s
>
</
p
>
</
subchap2
>
</
subchap1
>
</
chap
>
</
body
>
</
text
>
</
archimedes
>