Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
Text
Text Image
Image
XML
Thumbnail overview
Document information
None
Concordance
Figures
Thumbnails
List of thumbnails
<
1 - 10
11 - 20
21 - 30
31 - 40
41 - 50
51 - 60
61 - 70
71 - 80
81 - 90
91 - 100
101 - 110
111 - 120
121 - 130
131 - 140
141 - 150
151 - 160
161 - 170
171 - 180
181 - 190
191 - 200
201 - 210
211 - 220
221 - 230
231 - 240
241 - 250
251 - 260
261 - 270
271 - 280
281 - 290
291 - 300
301 - 310
311 - 320
321 - 330
331 - 340
341 - 350
351 - 360
361 - 370
371 - 380
381 - 390
391 - 400
401 - 410
411 - 420
421 - 430
431 - 440
441 - 450
451 - 460
461 - 470
471 - 480
481 - 490
491 - 500
501 - 510
511 - 520
521 - 524
>
71
72
73
74
75
76
77
78
79
80
<
1 - 10
11 - 20
21 - 30
31 - 40
41 - 50
51 - 60
61 - 70
71 - 80
81 - 90
91 - 100
101 - 110
111 - 120
121 - 130
131 - 140
141 - 150
151 - 160
161 - 170
171 - 180
181 - 190
191 - 200
201 - 210
211 - 220
221 - 230
231 - 240
241 - 250
251 - 260
261 - 270
271 - 280
281 - 290
291 - 300
301 - 310
311 - 320
321 - 330
331 - 340
341 - 350
351 - 360
361 - 370
371 - 380
381 - 390
391 - 400
401 - 410
411 - 420
421 - 430
431 - 440
441 - 450
451 - 460
461 - 470
471 - 480
481 - 490
491 - 500
501 - 510
511 - 520
521 - 524
>
page
|<
<
of 524
>
>|
<
archimedes
>
<
text
>
<
body
>
<
chap
>
<
subchap1
>
<
subchap2
>
<
p
type
="
main
">
<
s
>
<
pb
xlink:href
="
039/01/090.jpg
"
pagenum
="
62
"/>
<
arrow.to.target
n
="
note38
"/>
ut
<
emph
type
="
italics
"/>
Vk-VK
<
emph.end
type
="
italics
"/>
ad
<
emph
type
="
italics
"/>
kS-KS,
<
emph.end
type
="
italics
"/>
id eſt ut 2
<
emph
type
="
italics
"/>
VX
<
emph.end
type
="
italics
"/>
ad 2
<
emph
type
="
italics
"/>
KX
<
emph.end
type
="
italics
"/>
& 2
<
emph
type
="
italics
"/>
KX
<
emph.end
type
="
italics
"/>
ad
<
lb
/>
2
<
emph
type
="
italics
"/>
SX,
<
emph.end
type
="
italics
"/>
adeoque ut
<
emph
type
="
italics
"/>
VX
<
emph.end
type
="
italics
"/>
ad
<
emph
type
="
italics
"/>
HX
<
emph.end
type
="
italics
"/>
&
<
emph
type
="
italics
"/>
HX
<
emph.end
type
="
italics
"/>
ad
<
emph
type
="
italics
"/>
SX,
<
emph.end
type
="
italics
"/>
ſimilia erunt tri
<
lb
/>
angula
<
emph
type
="
italics
"/>
VXH, HXS,
<
emph.end
type
="
italics
"/>
& propterea
<
emph
type
="
italics
"/>
VH
<
emph.end
type
="
italics
"/>
erit ad
<
emph
type
="
italics
"/>
SH
<
emph.end
type
="
italics
"/>
ut
<
emph
type
="
italics
"/>
VX
<
emph.end
type
="
italics
"/>
ad
<
emph
type
="
italics
"/>
XH,
<
emph.end
type
="
italics
"/>
<
lb
/>
adeoque ut
<
emph
type
="
italics
"/>
VK
<
emph.end
type
="
italics
"/>
ad
<
emph
type
="
italics
"/>
KS.
<
emph.end
type
="
italics
"/>
Habet igitur Trajectoriæ deſcriptæ axis
<
lb
/>
principalis
<
emph
type
="
italics
"/>
VH
<
emph.end
type
="
italics
"/>
eam rationem ad ipſius umbilieorum diſtantiam
<
emph
type
="
italics
"/>
SH,
<
emph.end
type
="
italics
"/>
<
lb
/>
quam habet Trajectoriæ deſcribendæ axis principalis ad ipſius um
<
lb
/>
bilieorum diſtantiam, & propterea ejuſdem eſt ſpeciei. </
s
>
<
s
>Inſuper cum
<
lb
/>
<
emph
type
="
italics
"/>
VH, vH
<
emph.end
type
="
italics
"/>
æquentur axi principali, &
<
emph
type
="
italics
"/>
VS, vS
<
emph.end
type
="
italics
"/>
a rectis
<
emph
type
="
italics
"/>
TR, tr
<
emph.end
type
="
italics
"/>
<
lb
/>
perpendiculariter biſecentur, liquet, ex Lemmate XV, rectas illas
<
lb
/>
Trajectoriam deſcriptam tangere.
<
emph
type
="
italics
"/>
q.E.F.
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
<
p
type
="
margin
">
<
s
>
<
margin.target
id
="
note38
"/>
DE MOTU
<
lb
/>
CORPORUM</
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
emph
type
="
italics
"/>
Cas.
<
emph.end
type
="
italics
"/>
3. Dato umbilico
<
emph
type
="
italics
"/>
S
<
emph.end
type
="
italics
"/>
deſcribenda ſit Trajectoria quæ rect
<
lb
/>
am
<
emph
type
="
italics
"/>
TR
<
emph.end
type
="
italics
"/>
tanget in puncto dato
<
emph
type
="
italics
"/>
R.
<
emph.end
type
="
italics
"/>
In rectam
<
emph
type
="
italics
"/>
TR
<
emph.end
type
="
italics
"/>
demitte perpen
<
lb
/>
dicularem
<
emph
type
="
italics
"/>
ST,
<
emph.end
type
="
italics
"/>
& produc eandem ad
<
emph
type
="
italics
"/>
V,
<
emph.end
type
="
italics
"/>
ut ſit
<
emph
type
="
italics
"/>
TV
<
emph.end
type
="
italics
"/>
æqualis
<
emph
type
="
italics
"/>
ST.
<
emph.end
type
="
italics
"/>
Junge
<
lb
/>
<
emph
type
="
italics
"/>
VR,
<
emph.end
type
="
italics
"/>
& rectam
<
emph
type
="
italics
"/>
VS
<
emph.end
type
="
italics
"/>
infinite productam ſeca in
<
emph
type
="
italics
"/>
K
<
emph.end
type
="
italics
"/>
&
<
emph
type
="
italics
"/>
k,
<
emph.end
type
="
italics
"/>
ita ut ſit
<
lb
/>
<
emph
type
="
italics
"/>
VK
<
emph.end
type
="
italics
"/>
ad
<
emph
type
="
italics
"/>
SK
<
emph.end
type
="
italics
"/>
&
<
emph
type
="
italics
"/>
Vk
<
emph.end
type
="
italics
"/>
ad
<
emph
type
="
italics
"/>
Sk
<
emph.end
type
="
italics
"/>
ut Ellipſeos deſcribendæ axis principalis
<
lb
/>
ad diſtantiam umbilieorum; circuloque ſuper diametro
<
emph
type
="
italics
"/>
Kk
<
emph.end
type
="
italics
"/>
de
<
lb
/>
ſcripto, ſecetur producta recta
<
emph
type
="
italics
"/>
VR
<
emph.end
type
="
italics
"/>
in
<
emph
type
="
italics
"/>
H,
<
emph.end
type
="
italics
"/>
& umbilicis
<
emph
type
="
italics
"/>
S, H,
<
emph.end
type
="
italics
"/>
axe
<
lb
/>
principali rectam
<
emph
type
="
italics
"/>
VH
<
emph.end
type
="
italics
"/>
æquante, deſcribatur Trajectoria. </
s
>
<
s
>Dico fa
<
lb
/>
ctum. </
s
>
<
s
>Namque
<
emph
type
="
italics
"/>
VH
<
emph.end
type
="
italics
"/>
eſſe ad
<
lb
/>
<
figure
id
="
id.039.01.090.1.jpg
"
xlink:href
="
039/01/090/1.jpg
"
number
="
33
"/>
<
lb
/>
<
emph
type
="
italics
"/>
SH
<
emph.end
type
="
italics
"/>
ut
<
emph
type
="
italics
"/>
VK
<
emph.end
type
="
italics
"/>
ad
<
emph
type
="
italics
"/>
SK,
<
emph.end
type
="
italics
"/>
atque adeo
<
lb
/>
ut axis principalis Trajectoriæ
<
lb
/>
deſcribendæ ad diſtantiam um
<
lb
/>
bilieorum ejus, patet ex demon
<
lb
/>
ſtratis in Caſu ſecundo, & prop
<
lb
/>
terea Trajectoriam deſcriptam
<
lb
/>
ejuſdem eſſe ſpeciei cum deſcri
<
lb
/>
benda; rectam vero
<
emph
type
="
italics
"/>
TR
<
emph.end
type
="
italics
"/>
qua an
<
lb
/>
gulus
<
emph
type
="
italics
"/>
VRS
<
emph.end
type
="
italics
"/>
biſecatur, tangere Trajectoriam in puncto
<
emph
type
="
italics
"/>
R,
<
emph.end
type
="
italics
"/>
patet ex
<
lb
/>
Conicis.
<
emph
type
="
italics
"/>
q.E.F.
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
emph
type
="
italics
"/>
Cas.
<
emph.end
type
="
italics
"/>
4. Circa umbilicum
<
emph
type
="
italics
"/>
S
<
emph.end
type
="
italics
"/>
deſcribenda jam ſit Trajectoria
<
emph
type
="
italics
"/>
APB,
<
emph.end
type
="
italics
"/>
<
lb
/>
quæ tangat rectam
<
emph
type
="
italics
"/>
TR,
<
emph.end
type
="
italics
"/>
tranſeatque per punctum quodvis
<
emph
type
="
italics
"/>
P
<
emph.end
type
="
italics
"/>
extra
<
lb
/>
tangentem datum, quæque ſimilis ſit Figuræ
<
emph
type
="
italics
"/>
apb,
<
emph.end
type
="
italics
"/>
axe principali
<
lb
/>
<
emph
type
="
italics
"/>
ab
<
emph.end
type
="
italics
"/>
& umbilicis
<
emph
type
="
italics
"/>
s, h
<
emph.end
type
="
italics
"/>
deſcriptæ. </
s
>
<
s
>In tangentem
<
emph
type
="
italics
"/>
TR
<
emph.end
type
="
italics
"/>
demitte per
<
lb
/>
pendiculum
<
emph
type
="
italics
"/>
ST,
<
emph.end
type
="
italics
"/>
& produc idem ad
<
emph
type
="
italics
"/>
V,
<
emph.end
type
="
italics
"/>
ut ſit
<
emph
type
="
italics
"/>
TV
<
emph.end
type
="
italics
"/>
æqualis
<
emph
type
="
italics
"/>
ST.
<
emph.end
type
="
italics
"/>
An
<
lb
/>
gulis autem
<
emph
type
="
italics
"/>
VSP, SVP
<
emph.end
type
="
italics
"/>
fac angulos
<
emph
type
="
italics
"/>
hsq, shq
<
emph.end
type
="
italics
"/>
æquales; cen
<
lb
/>
troque
<
emph
type
="
italics
"/>
q
<
emph.end
type
="
italics
"/>
& intervallo quod ſit ad
<
emph
type
="
italics
"/>
ab
<
emph.end
type
="
italics
"/>
ut
<
emph
type
="
italics
"/>
SP
<
emph.end
type
="
italics
"/>
ad
<
emph
type
="
italics
"/>
VS
<
emph.end
type
="
italics
"/>
deſcribe circu
<
lb
/>
lum ſecantem Figuram
<
emph
type
="
italics
"/>
apb
<
emph.end
type
="
italics
"/>
in
<
emph
type
="
italics
"/>
p.
<
emph.end
type
="
italics
"/>
Junge
<
emph
type
="
italics
"/>
sp
<
emph.end
type
="
italics
"/>
& age
<
emph
type
="
italics
"/>
SH
<
emph.end
type
="
italics
"/>
quæ ſit ad
<
lb
/>
<
emph
type
="
italics
"/>
sh
<
emph.end
type
="
italics
"/>
ut eſt
<
emph
type
="
italics
"/>
SP
<
emph.end
type
="
italics
"/>
ad
<
emph
type
="
italics
"/>
sp,
<
emph.end
type
="
italics
"/>
quæque angulum
<
emph
type
="
italics
"/>
PSH
<
emph.end
type
="
italics
"/>
angulo
<
emph
type
="
italics
"/>
psh
<
emph.end
type
="
italics
"/>
& angulum
<
lb
/>
<
emph
type
="
italics
"/>
VSH
<
emph.end
type
="
italics
"/>
angulo
<
emph
type
="
italics
"/>
psq
<
emph.end
type
="
italics
"/>
æquales conſtituat. </
s
>
<
s
>Denique umbilicis
<
emph
type
="
italics
"/>
S, H,
<
emph.end
type
="
italics
"/>
<
lb
/>
& axe principali
<
emph
type
="
italics
"/>
AB
<
emph.end
type
="
italics
"/>
diſtantiam
<
emph
type
="
italics
"/>
VH
<
emph.end
type
="
italics
"/>
æquante, deſcribatur ſectio
<
lb
/>
Conica. </
s
>
<
s
>Dico factum. </
s
>
<
s
>Nam ſi agatur
<
emph
type
="
italics
"/>
sv
<
emph.end
type
="
italics
"/>
quæ ſit ad
<
emph
type
="
italics
"/>
sp
<
emph.end
type
="
italics
"/>
ut eſt
<
emph
type
="
italics
"/>
sh
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
</
subchap2
>
</
subchap1
>
</
chap
>
</
body
>
</
text
>
</
archimedes
>