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
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
<
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
>
<
pb
xlink:href
="
039/01/095.jpg
"
pagenum
="
67
"/>
<
p
type
="
main
">
<
s
>
<
emph
type
="
italics
"/>
Cas.
<
emph.end
type
="
italics
"/>
2. Ponamus jam Trapezii latera oppoſita
<
emph
type
="
italics
"/>
AC
<
emph.end
type
="
italics
"/>
&
<
emph
type
="
italics
"/>
BD
<
emph.end
type
="
italics
"/>
non
<
lb
/>
<
arrow.to.target
n
="
note43
"/>
eſſe parallela. </
s
>
<
s
>Age
<
emph
type
="
italics
"/>
Bd
<
emph.end
type
="
italics
"/>
parallelam
<
emph
type
="
italics
"/>
AC
<
emph.end
type
="
italics
"/>
& occurrentem tum rectæ
<
lb
/>
<
emph
type
="
italics
"/>
ST
<
emph.end
type
="
italics
"/>
in
<
emph
type
="
italics
"/>
t,
<
emph.end
type
="
italics
"/>
tum Conicæ ſectioni in
<
emph
type
="
italics
"/>
d.
<
emph.end
type
="
italics
"/>
Junge
<
emph
type
="
italics
"/>
Cd
<
emph.end
type
="
italics
"/>
ſecantem
<
emph
type
="
italics
"/>
PQ
<
emph.end
type
="
italics
"/>
in
<
emph
type
="
italics
"/>
r,
<
emph.end
type
="
italics
"/>
<
lb
/>
& ipſi
<
emph
type
="
italics
"/>
PQ
<
emph.end
type
="
italics
"/>
parallelam age
<
emph
type
="
italics
"/>
DM
<
emph.end
type
="
italics
"/>
<
lb
/>
<
figure
id
="
id.039.01.095.1.jpg
"
xlink:href
="
039/01/095/1.jpg
"
number
="
39
"/>
<
lb
/>
ſecantem
<
emph
type
="
italics
"/>
Cd
<
emph.end
type
="
italics
"/>
in
<
emph
type
="
italics
"/>
M
<
emph.end
type
="
italics
"/>
&
<
emph
type
="
italics
"/>
AB
<
emph.end
type
="
italics
"/>
in
<
emph
type
="
italics
"/>
N.
<
emph.end
type
="
italics
"/>
<
lb
/>
Jam ob ſimilia triangula
<
emph
type
="
italics
"/>
BTt,
<
lb
/>
DBN
<
emph.end
type
="
italics
"/>
; eſt
<
emph
type
="
italics
"/>
Bt
<
emph.end
type
="
italics
"/>
ſeu
<
emph
type
="
italics
"/>
PQ
<
emph.end
type
="
italics
"/>
ad
<
emph
type
="
italics
"/>
Tt
<
emph.end
type
="
italics
"/>
ut
<
lb
/>
<
emph
type
="
italics
"/>
DN
<
emph.end
type
="
italics
"/>
ad
<
emph
type
="
italics
"/>
NB.
<
emph.end
type
="
italics
"/>
Sic &
<
emph
type
="
italics
"/>
Rr
<
emph.end
type
="
italics
"/>
eſt ad
<
lb
/>
<
emph
type
="
italics
"/>
AQ
<
emph.end
type
="
italics
"/>
ſeu
<
emph
type
="
italics
"/>
PS
<
emph.end
type
="
italics
"/>
ut
<
emph
type
="
italics
"/>
DM
<
emph.end
type
="
italics
"/>
ad
<
emph
type
="
italics
"/>
AN.
<
emph.end
type
="
italics
"/>
<
lb
/>
Ergo, ducendo antecedentes in
<
lb
/>
antecedentes & conſequentes in
<
lb
/>
conſequentes, ut rectangulum
<
emph
type
="
italics
"/>
PQ
<
emph.end
type
="
italics
"/>
<
lb
/>
in
<
emph
type
="
italics
"/>
Rr
<
emph.end
type
="
italics
"/>
eſt ad rectangulum
<
emph
type
="
italics
"/>
PS
<
emph.end
type
="
italics
"/>
in
<
lb
/>
<
emph
type
="
italics
"/>
Tt,
<
emph.end
type
="
italics
"/>
ita rectangulum
<
emph
type
="
italics
"/>
NDM
<
emph.end
type
="
italics
"/>
eſt
<
lb
/>
ad rectangulum
<
emph
type
="
italics
"/>
ANB,
<
emph.end
type
="
italics
"/>
& (per Caſ.1) ita rectangulum
<
emph
type
="
italics
"/>
PQ
<
emph.end
type
="
italics
"/>
in
<
emph
type
="
italics
"/>
Pr
<
emph.end
type
="
italics
"/>
eſt
<
lb
/>
ad rectangulum
<
emph
type
="
italics
"/>
PS
<
emph.end
type
="
italics
"/>
in
<
emph
type
="
italics
"/>
Pt,
<
emph.end
type
="
italics
"/>
ac diviſim ita rectangulum
<
emph
type
="
italics
"/>
PQXPR
<
emph.end
type
="
italics
"/>
<
lb
/>
eſt ad rectangulum
<
emph
type
="
italics
"/>
PSXPT. Q.E.D.
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
<
p
type
="
margin
">
<
s
>
<
margin.target
id
="
note43
"/>
LIBER
<
lb
/>
PRIMUS.</
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
emph
type
="
italics
"/>
Cas.
<
emph.end
type
="
italics
"/>
3. Ponamus denique lineas
<
lb
/>
<
figure
id
="
id.039.01.095.2.jpg
"
xlink:href
="
039/01/095/2.jpg
"
number
="
40
"/>
<
lb
/>
quatuor
<
emph
type
="
italics
"/>
PQ, PR, PS, PT
<
emph.end
type
="
italics
"/>
non
<
lb
/>
eſſe parallelas lateribus
<
emph
type
="
italics
"/>
AC, AB,
<
emph.end
type
="
italics
"/>
<
lb
/>
ſed ad ea utcunQ.E.I.clinatas. </
s
>
<
s
>Ea
<
lb
/>
rum vice age
<
emph
type
="
italics
"/>
Pq, Pr
<
emph.end
type
="
italics
"/>
parallelas
<
lb
/>
ipſi
<
emph
type
="
italics
"/>
AC
<
emph.end
type
="
italics
"/>
; &
<
emph
type
="
italics
"/>
Ps, Pt
<
emph.end
type
="
italics
"/>
parallelas
<
lb
/>
ipſi
<
emph
type
="
italics
"/>
AB
<
emph.end
type
="
italics
"/>
; & propter datos angu
<
lb
/>
los triangulorum
<
emph
type
="
italics
"/>
PQq, PRr,
<
lb
/>
PSs, PTt,
<
emph.end
type
="
italics
"/>
dabuntur rationes
<
lb
/>
<
emph
type
="
italics
"/>
PQ
<
emph.end
type
="
italics
"/>
ad
<
emph
type
="
italics
"/>
Pq, PR
<
emph.end
type
="
italics
"/>
ad
<
emph
type
="
italics
"/>
Pr, PS
<
emph.end
type
="
italics
"/>
<
lb
/>
ad
<
emph
type
="
italics
"/>
Ps,
<
emph.end
type
="
italics
"/>
&
<
emph
type
="
italics
"/>
PT
<
emph.end
type
="
italics
"/>
ad
<
emph
type
="
italics
"/>
Pt
<
emph.end
type
="
italics
"/>
; atque adeo rationes compoſitæ
<
emph
type
="
italics
"/>
PQXPR
<
emph.end
type
="
italics
"/>
<
lb
/>
ad
<
emph
type
="
italics
"/>
PqXPr,
<
emph.end
type
="
italics
"/>
&
<
emph
type
="
italics
"/>
PSXPT
<
emph.end
type
="
italics
"/>
ad
<
emph
type
="
italics
"/>
PsXPt.
<
emph.end
type
="
italics
"/>
Sed, per ſuperius de
<
lb
/>
monſtrata, ratio
<
emph
type
="
italics
"/>
PqXPr
<
emph.end
type
="
italics
"/>
ad
<
emph
type
="
italics
"/>
PsXPt
<
emph.end
type
="
italics
"/>
data eſt: Ergo & ratio
<
lb
/>
<
emph
type
="
italics
"/>
PQXPR
<
emph.end
type
="
italics
"/>
ad
<
emph
type
="
italics
"/>
PSXPT. Q.E.D.
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
emph
type
="
center
"/>
LEMMA XVIII.
<
emph.end
type
="
center
"/>
</
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
emph
type
="
italics
"/>
Iiſdem poſitis, ſi rectangulum ductarum ad oppoſita duo latera Tra
<
lb
/>
pezii
<
emph.end
type
="
italics
"/>
PQXPR
<
emph
type
="
italics
"/>
ſit ad rectangulum ductarum ad reliqua duo late
<
lb
/>
ra
<
emph.end
type
="
italics
"/>
PSXPT
<
emph
type
="
italics
"/>
in data ratione; punctum
<
emph.end
type
="
italics
"/>
P,
<
emph
type
="
italics
"/>
a quo lineæ ducuntur,
<
lb
/>
tanget Conicam ſectionem circa Trapezium deſcriptam.
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
</
subchap2
>
</
subchap1
>
</
chap
>
</
body
>
</
text
>
</
archimedes
>