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
="
039/01/260.jpg
"
pagenum
="
232
"/>
<
arrow.to.target
n
="
note208
"/>
Medio reſiſtente aſcendendo poſſit amittere, ad tempus quo velo
<
lb
/>
citatem eandem in ſpatio non reſiſtente aſcendendo poſſet amit
<
lb
/>
tere, ut arcus
<
emph
type
="
italics
"/>
At
<
emph.end
type
="
italics
"/>
ad ejus tangentem
<
emph
type
="
italics
"/>
Ap.
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
<
p
type
="
margin
">
<
s
>
<
margin.target
id
="
note208
"/>
DE MOTU
<
lb
/>
CORPORUM</
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
emph
type
="
italics
"/>
Corol.
<
emph.end
type
="
italics
"/>
6. Hinc ex dato tempore datur ſpatium aſcenſu vel de
<
lb
/>
ſcenſu deſcriptum. </
s
>
<
s
>Nam corporis in infinitum deſcendentis datur
<
lb
/>
velocitas maxima, per Corol. </
s
>
<
s
>2, & 3, Theor. </
s
>
<
s
>VI, Lib. </
s
>
<
s
>11; indeque
<
lb
/>
datur tempus quo corpus velocitatem illam in ſpatio non reſiſtente
<
lb
/>
cadendo poſſet acquirere. </
s
>
<
s
>Et ſumendo Sectorem
<
emph
type
="
italics
"/>
ADT
<
emph.end
type
="
italics
"/>
vel
<
emph
type
="
italics
"/>
ADt
<
emph.end
type
="
italics
"/>
<
lb
/>
ad triangulum
<
emph
type
="
italics
"/>
ADC
<
emph.end
type
="
italics
"/>
in ratione temporis dati ad tempus modo
<
lb
/>
inventum; dabitur tum velocitas
<
emph
type
="
italics
"/>
AP
<
emph.end
type
="
italics
"/>
vel
<
emph
type
="
italics
"/>
Ap,
<
emph.end
type
="
italics
"/>
tum area
<
emph
type
="
italics
"/>
ABNK
<
emph.end
type
="
italics
"/>
<
lb
/>
vel
<
emph
type
="
italics
"/>
ABnk,
<
emph.end
type
="
italics
"/>
quæ eſt ad ſectorem
<
emph
type
="
italics
"/>
ADT
<
emph.end
type
="
italics
"/>
vel
<
emph
type
="
italics
"/>
ADt
<
emph.end
type
="
italics
"/>
ut ſpatium quæ
<
lb
/>
ſitum ad ſpatium quod tempore dato, cum velocitate illa maxima
<
lb
/>
jam ante inventa, uniformiter deſcribi poteſt. </
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
emph
type
="
italics
"/>
Corol.
<
emph.end
type
="
italics
"/>
7. Et regrediendo, ex dato aſcenſus vel deſcenſus ſpatio
<
lb
/>
<
emph
type
="
italics
"/>
ABnk
<
emph.end
type
="
italics
"/>
vel
<
emph
type
="
italics
"/>
ABNK,
<
emph.end
type
="
italics
"/>
dabitur tempus
<
emph
type
="
italics
"/>
ADt
<
emph.end
type
="
italics
"/>
vel
<
emph
type
="
italics
"/>
ADT.
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
emph
type
="
center
"/>
PROPOSITIO X. PROBLEMA III.
<
emph.end
type
="
center
"/>
</
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
emph
type
="
italics
"/>
Tendat uniformis vis gravitatis directe ad planum Horizontis,
<
lb
/>
ſitque reſiſtentia ut Medii denſitas & quadratum velocitatis
<
lb
/>
conjunctim: requiritur tum Medii denſitas in locis ſingulis,
<
lb
/>
quæ faciat ut corpus in data quavis linea curva moveatur,
<
lb
/>
tum corporis velocitas & Medii reſiſtentia in locis ſingulis.
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
<
p
type
="
main
">
<
s
>Sit
<
emph
type
="
italics
"/>
PQ
<
emph.end
type
="
italics
"/>
planum illud pla
<
lb
/>
<
figure
id
="
id.039.01.260.1.jpg
"
xlink:href
="
039/01/260/1.jpg
"
number
="
153
"/>
<
lb
/>
no Schematis perpendicu
<
lb
/>
lare;
<
emph
type
="
italics
"/>
PFHQ
<
emph.end
type
="
italics
"/>
linea curva
<
lb
/>
plano huic occurrens in
<
lb
/>
punctis
<
emph
type
="
italics
"/>
P
<
emph.end
type
="
italics
"/>
&
<
emph
type
="
italics
"/>
<
expan
abbr
="
q;
">que</
expan
>
G, H, I, K
<
emph.end
type
="
italics
"/>
<
lb
/>
loca quatuor corporis in hac
<
lb
/>
curva ab
<
emph
type
="
italics
"/>
F
<
emph.end
type
="
italics
"/>
ad
<
emph
type
="
italics
"/>
Q
<
emph.end
type
="
italics
"/>
pergentis;
<
lb
/>
&
<
emph
type
="
italics
"/>
GB, HC, ID, KE
<
emph.end
type
="
italics
"/>
or
<
lb
/>
dinatæ quatuor parallelæ ab
<
lb
/>
his punctis ad horizontem
<
lb
/>
demiſſæ & lineæ horizontali
<
emph
type
="
italics
"/>
PQ
<
emph.end
type
="
italics
"/>
ad puncta
<
emph
type
="
italics
"/>
B, C, D, E
<
emph.end
type
="
italics
"/>
inſiſten
<
lb
/>
tes; & ſint
<
emph
type
="
italics
"/>
BC, CD, DE
<
emph.end
type
="
italics
"/>
diſtantiæ Ordinatarum inter ſe æqua
<
lb
/>
les. </
s
>
<
s
>A punctis
<
emph
type
="
italics
"/>
G
<
emph.end
type
="
italics
"/>
&
<
emph
type
="
italics
"/>
H
<
emph.end
type
="
italics
"/>
ducantur rectæ
<
emph
type
="
italics
"/>
GL, HN
<
emph.end
type
="
italics
"/>
curvam tan
<
lb
/>
gentes in
<
emph
type
="
italics
"/>
G
<
emph.end
type
="
italics
"/>
&
<
emph
type
="
italics
"/>
H,
<
emph.end
type
="
italics
"/>
& Ordinatis
<
emph
type
="
italics
"/>
CH, DI
<
emph.end
type
="
italics
"/>
ſurſum productis occur
<
lb
/>
rentes in
<
emph
type
="
italics
"/>
L
<
emph.end
type
="
italics
"/>
&
<
emph
type
="
italics
"/>
N,
<
emph.end
type
="
italics
"/>
& compleatur parallelogrammum
<
emph
type
="
italics
"/>
HCDM.
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
</
subchap2
>
</
subchap1
>
</
chap
>
</
body
>
</
text
>
</
archimedes
>