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
>
91
92
93
94
95
96
97
98
99
100
<
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
>
<
pb
xlink:href
="
039/01/096.jpg
"
pagenum
="
68
"/>
<
p
type
="
main
">
<
s
>Per puncta
<
emph
type
="
italics
"/>
A, B, C, D
<
emph.end
type
="
italics
"/>
& aliquod infinitorum punctorum
<
emph
type
="
italics
"/>
P,
<
emph.end
type
="
italics
"/>
pu
<
lb
/>
<
arrow.to.target
n
="
note44
"/>
ta
<
emph
type
="
italics
"/>
p,
<
emph.end
type
="
italics
"/>
concipe Conicam ſectionem deſcribi: dico punctum
<
emph
type
="
italics
"/>
P
<
emph.end
type
="
italics
"/>
hanc
<
lb
/>
ſemper tangere. </
s
>
<
s
>Si negas,
<
lb
/>
<
figure
id
="
id.039.01.096.1.jpg
"
xlink:href
="
039/01/096/1.jpg
"
number
="
41
"/>
<
lb
/>
junge
<
emph
type
="
italics
"/>
AP
<
emph.end
type
="
italics
"/>
ſecantem hanc
<
lb
/>
Conicam ſectionem alibi
<
lb
/>
quam in
<
emph
type
="
italics
"/>
P,
<
emph.end
type
="
italics
"/>
ſi fieri poteſt,
<
lb
/>
puta in
<
emph
type
="
italics
"/>
b.
<
emph.end
type
="
italics
"/>
Ergo ſi ab his
<
lb
/>
punctis
<
emph
type
="
italics
"/>
p
<
emph.end
type
="
italics
"/>
&
<
emph
type
="
italics
"/>
b
<
emph.end
type
="
italics
"/>
ducantur in
<
lb
/>
datis angulis ad latera Tra
<
lb
/>
pezii rectæ
<
emph
type
="
italics
"/>
pq, pr, ps, pt
<
emph.end
type
="
italics
"/>
<
lb
/>
&
<
emph
type
="
italics
"/>
bk, br, bſ, bd
<
emph.end
type
="
italics
"/>
; erit
<
lb
/>
ut
<
emph
type
="
italics
"/>
bkXb
<
emph.end
type
="
italics
"/>
r ad
<
emph
type
="
italics
"/>
bſXbd
<
emph.end
type
="
italics
"/>
ita
<
lb
/>
(per Lem. </
s
>
<
s
>XVII)
<
emph
type
="
italics
"/>
pqXpr
<
emph.end
type
="
italics
"/>
<
lb
/>
ad
<
emph
type
="
italics
"/>
psXpt,
<
emph.end
type
="
italics
"/>
& ita (per
<
lb
/>
Hypoth.)
<
emph
type
="
italics
"/>
PQXPR
<
emph.end
type
="
italics
"/>
ad
<
lb
/>
<
emph
type
="
italics
"/>
PSXPT.
<
emph.end
type
="
italics
"/>
Eſt & prop
<
lb
/>
ter ſimilitudinem Trapeziorum
<
emph
type
="
italics
"/>
bkAſ, PQAS,
<
emph.end
type
="
italics
"/>
ut
<
emph
type
="
italics
"/>
bk
<
emph.end
type
="
italics
"/>
ad
<
emph
type
="
italics
"/>
bſ
<
emph.end
type
="
italics
"/>
ita
<
lb
/>
<
emph
type
="
italics
"/>
PQ
<
emph.end
type
="
italics
"/>
ad
<
emph
type
="
italics
"/>
PS.
<
emph.end
type
="
italics
"/>
Quare, applicando terminos prioris proportionis ad
<
lb
/>
terminos correſpondentes hujus, erit
<
emph
type
="
italics
"/>
b
<
emph.end
type
="
italics
"/>
r ad
<
emph
type
="
italics
"/>
bd
<
emph.end
type
="
italics
"/>
ut
<
emph
type
="
italics
"/>
PR
<
emph.end
type
="
italics
"/>
ad
<
emph
type
="
italics
"/>
PT.
<
emph.end
type
="
italics
"/>
Er
<
lb
/>
go Trapezia æquiangula
<
emph
type
="
italics
"/>
Dr bd, DRPT
<
emph.end
type
="
italics
"/>
ſimilia ſunt, & eorum
<
lb
/>
diagonales
<
emph
type
="
italics
"/>
Db, DP
<
emph.end
type
="
italics
"/>
propterea coincidunt. </
s
>
<
s
>Incidit itaque
<
emph
type
="
italics
"/>
b
<
emph.end
type
="
italics
"/>
in
<
lb
/>
interſectionem rectarum
<
emph
type
="
italics
"/>
AP, DP
<
emph.end
type
="
italics
"/>
adeoque coincidit cum puncto
<
lb
/>
<
emph
type
="
italics
"/>
P.
<
emph.end
type
="
italics
"/>
Quare punctum
<
emph
type
="
italics
"/>
P,
<
emph.end
type
="
italics
"/>
ubicunque ſumatur, incidit in aſſignatam
<
lb
/>
Conicam ſectionem.
<
emph
type
="
italics
"/>
Q.E.D.
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
<
p
type
="
margin
">
<
s
>
<
margin.target
id
="
note44
"/>
DE MOTU
<
lb
/>
CORPORUM</
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
emph
type
="
italics
"/>
Corol.
<
emph.end
type
="
italics
"/>
Hinc ſi rectæ tres
<
emph
type
="
italics
"/>
PQ, PR, PS
<
emph.end
type
="
italics
"/>
a puncto communi
<
emph
type
="
italics
"/>
P
<
emph.end
type
="
italics
"/>
<
lb
/>
ad alias totidem poſitione datas rectas
<
emph
type
="
italics
"/>
AB, CD, AC,
<
emph.end
type
="
italics
"/>
ſingulæ ad
<
lb
/>
ſingulas, in datis angulis ducantur, ſitque rectangulum ſub duabus
<
lb
/>
ductis
<
emph
type
="
italics
"/>
PQXPR
<
emph.end
type
="
italics
"/>
ad quadratum tertiæ
<
emph
type
="
italics
"/>
PS quad.
<
emph.end
type
="
italics
"/>
in data ratione:
<
lb
/>
punctum
<
emph
type
="
italics
"/>
P,
<
emph.end
type
="
italics
"/>
a quibus rectæ ducuntur, locabitur in ſectione Conica
<
lb
/>
quæ tangit lineas
<
emph
type
="
italics
"/>
AB, CD
<
emph.end
type
="
italics
"/>
in
<
emph
type
="
italics
"/>
A
<
emph.end
type
="
italics
"/>
&
<
emph
type
="
italics
"/>
C
<
emph.end
type
="
italics
"/>
; & contra. </
s
>
<
s
>Nam coeat linea
<
lb
/>
<
emph
type
="
italics
"/>
BD
<
emph.end
type
="
italics
"/>
cum linea
<
emph
type
="
italics
"/>
AC
<
emph.end
type
="
italics
"/>
manente poſitione trium
<
emph
type
="
italics
"/>
AB, CD, AC
<
emph.end
type
="
italics
"/>
; de
<
lb
/>
in coeat etiam linea
<
emph
type
="
italics
"/>
PT
<
emph.end
type
="
italics
"/>
cum linea
<
emph
type
="
italics
"/>
PS:
<
emph.end
type
="
italics
"/>
& rectangulum
<
emph
type
="
italics
"/>
PSXPT
<
emph.end
type
="
italics
"/>
<
lb
/>
evadet
<
emph
type
="
italics
"/>
PS quad.
<
emph.end
type
="
italics
"/>
rectæque
<
emph
type
="
italics
"/>
AB, CD
<
emph.end
type
="
italics
"/>
quæ curvam in punctis
<
emph
type
="
italics
"/>
A
<
emph.end
type
="
italics
"/>
&
<
emph
type
="
italics
"/>
B,
<
lb
/>
C
<
emph.end
type
="
italics
"/>
&
<
emph
type
="
italics
"/>
D
<
emph.end
type
="
italics
"/>
ſecabant, jam Curvam in punctis illis coeuntibus non am
<
lb
/>
plius ſecare poſſunt ſed tantum tangent. </
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
emph
type
="
center
"/>
<
emph
type
="
italics
"/>
Scholium.
<
emph.end
type
="
italics
"/>
<
emph.end
type
="
center
"/>
</
s
>
</
p
>
<
p
type
="
main
">
<
s
>Nomen Conicæ ſectionis in hoc Lemmate late ſumitur, ita ut
<
lb
/>
ſectio tam Rectilinea per verticem Coni tranſiens, quam Circularis
<
lb
/>
baſi parallela includatur. </
s
>
<
s
>Nam ſi punctum
<
emph
type
="
italics
"/>
p
<
emph.end
type
="
italics
"/>
incidit in rectam, qua
<
lb
/>
quævis ex punctis quatuor
<
emph
type
="
italics
"/>
A, B, C, D
<
emph.end
type
="
italics
"/>
junguntur, Conica ſectio </
s
>
</
p
>
</
subchap2
>
</
subchap1
>
</
chap
>
</
body
>
</
text
>
</
archimedes
>