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
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
<
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
="
039/01/270.jpg
"
pagenum
="
242
"/>
<
arrow.to.target
n
="
note218
"/>
</
s
>
</
p
>
<
p
type
="
margin
">
<
s
>
<
margin.target
id
="
note218
"/>
DE MOTU
<
lb
/>
CORPORUM</
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
emph
type
="
italics
"/>
Reg.
<
emph.end
type
="
italics
"/>
4. Quoniam denſitas Medii prope verticem Hyperbolæ
<
lb
/>
major eſt quam in loco
<
emph
type
="
italics
"/>
A,
<
emph.end
type
="
italics
"/>
ut habeatur denſitas mediocris, debet
<
lb
/>
ratio minimæ tangentium
<
emph
type
="
italics
"/>
GT
<
emph.end
type
="
italics
"/>
ad tangentem
<
emph
type
="
italics
"/>
AH
<
emph.end
type
="
italics
"/>
inveniri, &
<
lb
/>
denſitas in
<
emph
type
="
italics
"/>
A
<
emph.end
type
="
italics
"/>
angeri in ratione paudo majore quam ſemiſummæ
<
lb
/>
harum tangentium ad minimam tangentium
<
emph
type
="
italics
"/>
GT.
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
emph
type
="
italics
"/>
Reg.
<
emph.end
type
="
italics
"/>
5. Si dantur longitudines
<
emph
type
="
italics
"/>
AH, AI,
<
emph.end
type
="
italics
"/>
& deſcribenda ſit Figu
<
lb
/>
ra
<
emph
type
="
italics
"/>
AGK:
<
emph.end
type
="
italics
"/>
produc
<
emph
type
="
italics
"/>
HN
<
emph.end
type
="
italics
"/>
ad
<
emph
type
="
italics
"/>
X,
<
emph.end
type
="
italics
"/>
ut ſit
<
emph
type
="
italics
"/>
HX
<
emph.end
type
="
italics
"/>
æqualis facto ſub
<
emph
type
="
italics
"/>
n
<
emph.end
type
="
italics
"/>
+1 &
<
lb
/>
<
emph
type
="
italics
"/>
AI
<
emph.end
type
="
italics
"/>
; centroque
<
emph
type
="
italics
"/>
X
<
emph.end
type
="
italics
"/>
& Aſymptotis
<
emph
type
="
italics
"/>
MX, NX
<
emph.end
type
="
italics
"/>
per punctum
<
emph
type
="
italics
"/>
A
<
emph.end
type
="
italics
"/>
deſcriba
<
lb
/>
tur Hyperbola, ea lege, ut ſit
<
emph
type
="
italics
"/>
AI
<
emph.end
type
="
italics
"/>
ad quamvis
<
emph
type
="
italics
"/>
VG
<
emph.end
type
="
italics
"/>
ut
<
emph
type
="
italics
"/>
XV
<
emph
type
="
sup
"/>
n
<
emph.end
type
="
sup
"/>
<
emph.end
type
="
italics
"/>
ad
<
emph
type
="
italics
"/>
XI
<
emph
type
="
sup
"/>
n
<
emph.end
type
="
sup
"/>
.
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
emph
type
="
italics
"/>
Reg.
<
emph.end
type
="
italics
"/>
6. Quo major eſt numerus
<
emph
type
="
italics
"/>
n,
<
emph.end
type
="
italics
"/>
eo magis accuratæ ſunt hæ
<
lb
/>
Hyperbolæ in aſcenſu corporis ab
<
emph
type
="
italics
"/>
A,
<
emph.end
type
="
italics
"/>
& minus accuratæ in ejus de
<
lb
/>
ſcenſu ad
<
emph
type
="
italics
"/>
K
<
emph.end
type
="
italics
"/>
; & contra. </
s
>
<
s
>Hyperbola Conica mediocrem rationem
<
lb
/>
tenet, eſt que cæteris ſimplicior. </
s
>
<
s
>Igitur ſi Hyperbola ſit hujus generis,
<
lb
/>
& punctum
<
emph
type
="
italics
"/>
K,
<
emph.end
type
="
italics
"/>
ubi corpus projectum incidet in rectam quamvis
<
emph
type
="
italics
"/>
AN
<
emph.end
type
="
italics
"/>
<
lb
/>
per punctum
<
emph
type
="
italics
"/>
A
<
emph.end
type
="
italics
"/>
tranſeuntem, quæratur: occurrat producta
<
emph
type
="
italics
"/>
AN
<
emph.end
type
="
italics
"/>
<
lb
/>
Aſymptotis
<
emph
type
="
italics
"/>
MX, NX
<
emph.end
type
="
italics
"/>
in
<
emph
type
="
italics
"/>
M
<
emph.end
type
="
italics
"/>
&
<
emph
type
="
italics
"/>
N,
<
emph.end
type
="
italics
"/>
& ſumatur
<
emph
type
="
italics
"/>
NK
<
emph.end
type
="
italics
"/>
ipſi
<
emph
type
="
italics
"/>
AM
<
emph.end
type
="
italics
"/>
æqualis. </
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
emph
type
="
italics
"/>
Reg.
<
emph.end
type
="
italics
"/>
7. Et hinc liquet methodus expedita determinandi hanc
<
lb
/>
Hyperbolam ex Phænomenis. </
s
>
<
s
>Projiciantur corpora duo ſimilia &
<
lb
/>
æqualia, eadem velocitate, in angulis diverſis
<
emph
type
="
italics
"/>
HAK, hAk,
<
emph.end
type
="
italics
"/>
inci
<
lb
/>
dantQ.E.I. planum Horizontis in
<
emph
type
="
italics
"/>
K
<
emph.end
type
="
italics
"/>
&
<
emph
type
="
italics
"/>
k
<
emph.end
type
="
italics
"/>
; & notetur proportio
<
emph
type
="
italics
"/>
AK
<
emph.end
type
="
italics
"/>
<
lb
/>
ad
<
emph
type
="
italics
"/>
Ak.
<
emph.end
type
="
italics
"/>
Sit ea
<
emph
type
="
italics
"/>
d
<
emph.end
type
="
italics
"/>
ad
<
emph
type
="
italics
"/>
e.
<
emph.end
type
="
italics
"/>
Tum erecto cujuſvis longitudinis perpen
<
lb
/>
diculo
<
emph
type
="
italics
"/>
AI,
<
emph.end
type
="
italics
"/>
aſſume utcunque longitudinem
<
emph
type
="
italics
"/>
AH
<
emph.end
type
="
italics
"/>
vel
<
emph
type
="
italics
"/>
Ah,
<
emph.end
type
="
italics
"/>
& inde
<
lb
/>
collige graphice longitudines
<
emph
type
="
italics
"/>
AK, Ak,
<
emph.end
type
="
italics
"/>
per Reg. </
s
>
<
s
>6. Si ratio
<
emph
type
="
italics
"/>
AK
<
emph.end
type
="
italics
"/>
<
lb
/>
ad
<
emph
type
="
italics
"/>
Ak
<
emph.end
type
="
italics
"/>
ſit eadem cum ratione
<
emph
type
="
italics
"/>
d
<
emph.end
type
="
italics
"/>
ad
<
emph
type
="
italics
"/>
e,
<
emph.end
type
="
italics
"/>
longitudo
<
emph
type
="
italics
"/>
AH
<
emph.end
type
="
italics
"/>
recte aſſump
<
lb
/>
ta fuit. </
s
>
<
s
>Sin minus cape in recta infinita
<
emph
type
="
italics
"/>
SM
<
emph.end
type
="
italics
"/>
longitudinem
<
emph
type
="
italics
"/>
SM
<
emph.end
type
="
italics
"/>
<
lb
/>
æqualem aſſumptæ
<
emph
type
="
italics
"/>
AH,
<
emph.end
type
="
italics
"/>
& erige perpendiculum
<
emph
type
="
italics
"/>
MN
<
emph.end
type
="
italics
"/>
æquale ra
<
lb
/>
tionum differentiæ
<
emph
type
="
italics
"/>
(AK/Ak)-d/e
<
emph.end
type
="
italics
"/>
ductæ in rectam quamvis datam. </
s
>
<
s
>Si
<
lb
/>
mili methodo ex aſſumptis pluribus longitudinibus
<
emph
type
="
italics
"/>
AH
<
emph.end
type
="
italics
"/>
invenien
<
lb
/>
da ſunt plura puncta
<
emph
type
="
italics
"/>
N,
<
emph.end
type
="
italics
"/>
& per omnia a
<
lb
/>
<
figure
id
="
id.039.01.270.1.jpg
"
xlink:href
="
039/01/270/1.jpg
"
number
="
157
"/>
<
lb
/>
genda Curva linea regularis
<
emph
type
="
italics
"/>
NNXN,
<
emph.end
type
="
italics
"/>
ſe
<
lb
/>
cans rectam
<
emph
type
="
italics
"/>
SMMM
<
emph.end
type
="
italics
"/>
in
<
emph
type
="
italics
"/>
X.
<
emph.end
type
="
italics
"/>
Aſſumatur
<
lb
/>
demum
<
emph
type
="
italics
"/>
AH
<
emph.end
type
="
italics
"/>
æqualie abſciſſæ
<
emph
type
="
italics
"/>
SX
<
emph.end
type
="
italics
"/>
& inde
<
lb
/>
denuo inveniatur longitudo
<
emph
type
="
italics
"/>
AK
<
emph.end
type
="
italics
"/>
; & lon
<
lb
/>
gitudines, quæ ſint ad aſſumptam longitu
<
lb
/>
dinem
<
emph
type
="
italics
"/>
AI
<
emph.end
type
="
italics
"/>
& hanc ultimam
<
emph
type
="
italics
"/>
AH
<
emph.end
type
="
italics
"/>
ut longitudo
<
emph
type
="
italics
"/>
AK
<
emph.end
type
="
italics
"/>
per experi
<
lb
/>
mentum cognita ad ultimo inventam longitudinem
<
emph
type
="
italics
"/>
AK,
<
emph.end
type
="
italics
"/>
erunt veræ
<
lb
/>
illæ longitudines
<
emph
type
="
italics
"/>
AI
<
emph.end
type
="
italics
"/>
&
<
emph
type
="
italics
"/>
AH,
<
emph.end
type
="
italics
"/>
quas invenire oportuit. </
s
>
<
s
>Hiſce vero
<
lb
/>
datis dabitur & reſiſtentia Medii in loco
<
emph
type
="
italics
"/>
A,
<
emph.end
type
="
italics
"/>
quippe quæ ſit ad vim
<
lb
/>
gravitatis ut
<
emph
type
="
italics
"/>
AH
<
emph.end
type
="
italics
"/>
ad 2
<
emph
type
="
italics
"/>
AI.
<
emph.end
type
="
italics
"/>
Augenda eſt autem denſitas. </
s
>
<
s
>Medii per
<
lb
/>
Reg. </
s
>
<
s
>4; & reſiſtentia modo inventa, ſi in eadem ratione augeatur, fiet
<
lb
/>
accuratior. </
s
>
</
p
>
</
subchap2
>
</
subchap1
>
</
chap
>
</
body
>
</
text
>
</
archimedes
>