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
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
<
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
="
039/01/071.jpg
"
pagenum
="
43
"/>
ac denique per punctum
<
emph
type
="
italics
"/>
Q
<
emph.end
type
="
italics
"/>
agatur
<
emph
type
="
italics
"/>
LR
<
emph.end
type
="
italics
"/>
quæ ipſi
<
emph
type
="
italics
"/>
SP
<
emph.end
type
="
italics
"/>
parallela
<
lb
/>
ſit & occurrat tum circulo in
<
emph
type
="
italics
"/>
L
<
emph.end
type
="
italics
"/>
tum tangenti
<
emph
type
="
italics
"/>
PZ
<
emph.end
type
="
italics
"/>
in
<
emph
type
="
italics
"/>
R.
<
emph.end
type
="
italics
"/>
Et
<
lb
/>
ob ſimilia triangula
<
emph
type
="
italics
"/>
ZQR, ZTP, VPA
<
emph.end
type
="
italics
"/>
; erit
<
emph
type
="
italics
"/>
RP quad.
<
emph.end
type
="
italics
"/>
hoc
<
lb
/>
eſt
<
emph
type
="
italics
"/>
QRL
<
emph.end
type
="
italics
"/>
ad
<
emph
type
="
italics
"/>
QT quad.
<
emph.end
type
="
italics
"/>
ut
<
emph
type
="
italics
"/>
AV quad.
<
emph.end
type
="
italics
"/>
ad
<
emph
type
="
italics
"/>
PV quad.
<
emph.end
type
="
italics
"/>
Ideoque
<
lb
/>
(
<
emph
type
="
italics
"/>
QRLXPV quad./AV quad.
<
emph.end
type
="
italics
"/>
) æquatur
<
emph
type
="
italics
"/>
QT quad.
<
emph.end
type
="
italics
"/>
Ducantur hæc æqualia in
<
lb
/>
(
<
emph
type
="
italics
"/>
SP quad./QR
<
emph.end
type
="
italics
"/>
) &, punctis
<
emph
type
="
italics
"/>
P
<
emph.end
type
="
italics
"/>
&
<
emph
type
="
italics
"/>
Q
<
emph.end
type
="
italics
"/>
coeuntibus, ſcribatur
<
emph
type
="
italics
"/>
PV
<
emph.end
type
="
italics
"/>
pro
<
emph
type
="
italics
"/>
RL.
<
emph.end
type
="
italics
"/>
<
lb
/>
Sic fiet (
<
emph
type
="
italics
"/>
SP quad.XPV cub./AV quad.
<
emph.end
type
="
italics
"/>
) æquale (
<
emph
type
="
italics
"/>
SP quad.XQT quad./QR
<
emph.end
type
="
italics
"/>
) Ergo (per
<
lb
/>
Corol.1 & 5 Prop.VI.) vis centripeta eſt reciproce ut (
<
emph
type
="
italics
"/>
SPqXPV cub./AV quad
<
emph.end
type
="
italics
"/>
)
<
lb
/>
id eſt, (ob datum
<
emph
type
="
italics
"/>
AV quad.
<
emph.end
type
="
italics
"/>
) reciproce ut quadratum diſtantiæ ſeu
<
lb
/>
altitudinis
<
emph
type
="
italics
"/>
SP
<
emph.end
type
="
italics
"/>
& cubus chordæ
<
emph
type
="
italics
"/>
PV
<
emph.end
type
="
italics
"/>
conjunctim.
<
emph
type
="
italics
"/>
Q.E.I.
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
emph
type
="
center
"/>
<
emph
type
="
italics
"/>
Idem aliter.
<
emph.end
type
="
italics
"/>
<
emph.end
type
="
center
"/>
</
s
>
</
p
>
<
p
type
="
main
">
<
s
>Ad tangentem
<
emph
type
="
italics
"/>
PR
<
emph.end
type
="
italics
"/>
productam demittatur perpendiculum
<
emph
type
="
italics
"/>
SY,
<
emph.end
type
="
italics
"/>
<
lb
/>
& ob ſimilia triangula
<
emph
type
="
italics
"/>
SYP, VPA
<
emph.end
type
="
italics
"/>
; erit
<
emph
type
="
italics
"/>
AV
<
emph.end
type
="
italics
"/>
ad
<
emph
type
="
italics
"/>
PV
<
emph.end
type
="
italics
"/>
ut
<
emph
type
="
italics
"/>
SP
<
emph.end
type
="
italics
"/>
ad
<
lb
/>
<
emph
type
="
italics
"/>
SY,
<
emph.end
type
="
italics
"/>
ideoque (
<
emph
type
="
italics
"/>
SPXPV/AV
<
emph.end
type
="
italics
"/>
) æquale
<
emph
type
="
italics
"/>
SY,
<
emph.end
type
="
italics
"/>
& (
<
emph
type
="
italics
"/>
SP quad.XPV cub./AV quad.
<
emph.end
type
="
italics
"/>
) æquale
<
lb
/>
<
emph
type
="
italics
"/>
SY quad.XPV.
<
emph.end
type
="
italics
"/>
Et propterea (per Corol.3 & 5 Prop.VI.) vis centri
<
lb
/>
peta eſt reciproce ut (
<
emph
type
="
italics
"/>
SPqXPV cub./AVq
<
emph.end
type
="
italics
"/>
) hoc eſt, ob datam
<
emph
type
="
italics
"/>
AV,
<
emph.end
type
="
italics
"/>
reci
<
lb
/>
proce ut
<
emph
type
="
italics
"/>
SPqXPV cub. </
s
>
<
s
>
<
expan
abbr
="
q.
">que</
expan
>
E. I.
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
emph
type
="
italics
"/>
Corol.
<
emph.end
type
="
italics
"/>
1. Hinc ſi punctum datum
<
emph
type
="
italics
"/>
S
<
emph.end
type
="
italics
"/>
ad quod vis centripeta ſem
<
lb
/>
per tendit, locetur in circumferentia hujus circuli, puta ad
<
emph
type
="
italics
"/>
V
<
emph.end
type
="
italics
"/>
; erit
<
lb
/>
vis centripeta reciproce ut quadrato cubus altitudinis
<
emph
type
="
italics
"/>
SP.
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
emph
type
="
italics
"/>
Corol.
<
emph.end
type
="
italics
"/>
2. Vis qua corpus
<
emph
type
="
italics
"/>
P
<
emph.end
type
="
italics
"/>
in cir
<
lb
/>
<
figure
id
="
id.039.01.071.1.jpg
"
xlink:href
="
039/01/071/1.jpg
"
number
="
17
"/>
<
lb
/>
culo
<
emph
type
="
italics
"/>
APTV
<
emph.end
type
="
italics
"/>
circum virium centrum
<
lb
/>
<
emph
type
="
italics
"/>
S
<
emph.end
type
="
italics
"/>
revolvitur, eſt ad vim qua corpus
<
lb
/>
idem
<
emph
type
="
italics
"/>
P
<
emph.end
type
="
italics
"/>
in eodem circulo & eodem
<
lb
/>
tempore periodico circum aliud quod
<
lb
/>
vis virium centrum
<
emph
type
="
italics
"/>
R
<
emph.end
type
="
italics
"/>
revolvi poteſt,
<
lb
/>
ut
<
emph
type
="
italics
"/>
RP quad.XSP
<
emph.end
type
="
italics
"/>
ad cubum rectæ
<
emph
type
="
italics
"/>
SG
<
emph.end
type
="
italics
"/>
<
lb
/>
quæ a primo virium centro
<
emph
type
="
italics
"/>
S
<
emph.end
type
="
italics
"/>
ad or
<
lb
/>
bis tangentem
<
emph
type
="
italics
"/>
PG
<
emph.end
type
="
italics
"/>
ducitur, & diſtan
<
lb
/>
tiæ corporis a ſecundo virium centro
<
lb
/>
parallela eſt. </
s
>
<
s
>Nam, per conſtructionem hujus Propoſitionis, vis
<
lb
/>
prior eſt ad vim poſteriorem, ut
<
emph
type
="
italics
"/>
RPqXPT cub.
<
emph.end
type
="
italics
"/>
ad
<
emph
type
="
italics
"/>
SPqXPV cub.
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
</
subchap2
>
</
subchap1
>
</
chap
>
</
body
>
</
text
>
</
archimedes
>