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
="
039/01/274.jpg
"
pagenum
="
246
"/>
<
arrow.to.target
n
="
note222
"/>
velocitas, altera ut quadratum velocitatis: & ipſius (1/
<
emph
type
="
italics
"/>
GD
<
emph.end
type
="
italics
"/>
) decremen
<
lb
/>
tum eſt ut ſumma quantitatum (1/
<
emph
type
="
italics
"/>
GD
<
emph.end
type
="
italics
"/>
) & (
<
emph
type
="
italics
"/>
CG/GDq
<
emph.end
type
="
italics
"/>
), quarum prior eſt
<
lb
/>
ipſa (1/
<
emph
type
="
italics
"/>
GD
<
emph.end
type
="
italics
"/>
), & poſterior (
<
emph
type
="
italics
"/>
CG/GDq
<
emph.end
type
="
italics
"/>
) eſt ut (1/
<
emph
type
="
italics
"/>
GDq
<
emph.end
type
="
italics
"/>
). Proinde (1/
<
emph
type
="
italics
"/>
GD
<
emph.end
type
="
italics
"/>
), ob an
<
lb
/>
alogum decrementum, eſt ut velocitas. </
s
>
<
s
>Et ſi quantitas
<
emph
type
="
italics
"/>
GD,
<
emph.end
type
="
italics
"/>
ipſi (1/
<
emph
type
="
italics
"/>
GD
<
emph.end
type
="
italics
"/>
)
<
lb
/>
reciproce proportionalis, quantitate data
<
emph
type
="
italics
"/>
CG
<
emph.end
type
="
italics
"/>
augeatur; ſumma
<
emph
type
="
italics
"/>
CD,
<
emph.end
type
="
italics
"/>
<
lb
/>
tempore
<
emph
type
="
italics
"/>
ABED
<
emph.end
type
="
italics
"/>
uniformiter creſcente, creſcet in progreſſione
<
lb
/>
Geometrica.
<
emph
type
="
italics
"/>
Q.E.D.
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
<
p
type
="
margin
">
<
s
>
<
margin.target
id
="
note222
"/>
DE MOTU
<
lb
/>
CORPORUM</
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
emph
type
="
italics
"/>
Corol.
<
emph.end
type
="
italics
"/>
1. Igitur. </
s
>
<
s
>ſi, datis punctis
<
emph
type
="
italics
"/>
A, G,
<
emph.end
type
="
italics
"/>
exponatur tempus per
<
lb
/>
aream Hyperbolicam
<
emph
type
="
italics
"/>
ABED,
<
emph.end
type
="
italics
"/>
exponi poteſt velocitas per ipſius
<
lb
/>
<
emph
type
="
italics
"/>
GD
<
emph.end
type
="
italics
"/>
reciprocam (1/
<
emph
type
="
italics
"/>
GD
<
emph.end
type
="
italics
"/>
). </
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
emph
type
="
italics
"/>
Corol.
<
emph.end
type
="
italics
"/>
2. Sumendo autem
<
emph
type
="
italics
"/>
GA
<
emph.end
type
="
italics
"/>
ad
<
emph
type
="
italics
"/>
GD
<
emph.end
type
="
italics
"/>
ut velocitatis reciproca ſub
<
lb
/>
initio, ad velocitatis reciprocam in fine temporis cujuſvis
<
emph
type
="
italics
"/>
ABED,
<
emph.end
type
="
italics
"/>
<
lb
/>
invenietur punctum
<
emph
type
="
italics
"/>
G.
<
emph.end
type
="
italics
"/>
Eo autem invento, velocitas ex dato quo
<
lb
/>
vis alio tempore inveniri poteſt. </
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
emph
type
="
center
"/>
PROPOSITIO XII. THEOREMA IX.
<
emph.end
type
="
center
"/>
</
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
emph
type
="
italics
"/>
Iiſdem poſitis, dico quod ſi ſpatia deſcripta ſumantur in progreſſio
<
lb
/>
ne Arithmetica, velocitates data quadam quantitate auctæ e
<
lb
/>
runt in progreſſione Geometrica.
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
<
p
type
="
main
">
<
s
>In Aſymptoto
<
emph
type
="
italics
"/>
CD
<
emph.end
type
="
italics
"/>
detur pun
<
lb
/>
<
figure
id
="
id.039.01.274.1.jpg
"
xlink:href
="
039/01/274/1.jpg
"
number
="
161
"/>
<
lb
/>
ctum
<
emph
type
="
italics
"/>
R,
<
emph.end
type
="
italics
"/>
& erecto perpendiculo
<
emph
type
="
italics
"/>
RS,
<
emph.end
type
="
italics
"/>
<
lb
/>
quod occurrat Hyperbolæ in
<
emph
type
="
italics
"/>
S,
<
emph.end
type
="
italics
"/>
ex
<
lb
/>
ponatur deſcriptum ſpatium per a
<
lb
/>
ream Hyperbolicam
<
emph
type
="
italics
"/>
RSED
<
emph.end
type
="
italics
"/>
; &
<
lb
/>
velocitas erit ut longitudo
<
emph
type
="
italics
"/>
GD,
<
emph.end
type
="
italics
"/>
<
lb
/>
quæ cum data
<
emph
type
="
italics
"/>
CG
<
emph.end
type
="
italics
"/>
componit longi
<
lb
/>
tudinem
<
emph
type
="
italics
"/>
CD,
<
emph.end
type
="
italics
"/>
in progreſſione Geo
<
lb
/>
metrica decreſcentem, interea dum
<
lb
/>
ſpatium
<
emph
type
="
italics
"/>
RSED
<
emph.end
type
="
italics
"/>
augetur in Arith
<
lb
/>
metica. </
s
>
</
p
>
<
p
type
="
main
">
<
s
>Etenim ob datum ſpatii incrementum
<
emph
type
="
italics
"/>
EDde,
<
emph.end
type
="
italics
"/>
lineola
<
emph
type
="
italics
"/>
Dd,
<
emph.end
type
="
italics
"/>
quæ </
s
>
</
p
>
</
subchap2
>
</
subchap1
>
</
chap
>
</
body
>
</
text
>
</
archimedes
>