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
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
<
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
="
039/01/156.jpg
"
pagenum
="
128
"/>
<
arrow.to.target
n
="
note104
"/>
ut 1 ad √
<
emph
type
="
italics
"/>
n.
<
emph.end
type
="
italics
"/>
Quare cum angulus
<
emph
type
="
italics
"/>
VCP,
<
emph.end
type
="
italics
"/>
in deſcenſu corporis
<
lb
/>
ab Apſide ſumma ad Apſidem imam in Ellipſi confectus, ſit
<
lb
/>
graduum 180; conficietur angulus
<
emph
type
="
italics
"/>
VCp,
<
emph.end
type
="
italics
"/>
in deſcenſu corporis
<
lb
/>
ab Apſide ſumma ad Apſidem imam, in Orbe propemodum Cir
<
lb
/>
culari quem corpus quodvis vi centripeta dignitati A
<
emph
type
="
sup
"/>
<
emph
type
="
italics
"/>
n
<
emph.end
type
="
italics
"/>
-3
<
emph.end
type
="
sup
"/>
pro
<
lb
/>
portionali deſcribit, æqualis angulo graduum (180/√
<
emph
type
="
italics
"/>
n
<
emph.end
type
="
italics
"/>
); & hoc angulo
<
lb
/>
repetito corpus redibit ab Apſide ima ad Apſidem ſummam, &
<
lb
/>
ſic deinceps in infinitum. </
s
>
<
s
>Ut ſi vis centripeta ſit ut diſtantia cor
<
lb
/>
poris a centro, id eſt, ut A ſeu (A
<
emph
type
="
sup
"/>
4
<
emph.end
type
="
sup
"/>
/A
<
emph
type
="
sup
"/>
3
<
emph.end
type
="
sup
"/>
), erit
<
emph
type
="
italics
"/>
n
<
emph.end
type
="
italics
"/>
æqualis 4 & √
<
emph
type
="
italics
"/>
n
<
emph.end
type
="
italics
"/>
æqualis 2;
<
lb
/>
adeoque angulus inter Apſidem ſummam & Apſidem imam æ
<
lb
/>
qualis (180/2)
<
emph
type
="
italics
"/>
gr.
<
emph.end
type
="
italics
"/>
ſeu 90
<
emph
type
="
italics
"/>
gr.
<
emph.end
type
="
italics
"/>
Completa igitur quarta parte revolutio
<
lb
/>
nis unius corpus perveniet ad Apſidem imam, & completa alia
<
lb
/>
quarta parte ad Apſidem ſummam, & ſic deinceps per vices in
<
lb
/>
infinitum. </
s
>
<
s
>Id quod etiam ex Propoſitione x. </
s
>
<
s
>manifeſtum eſt. </
s
>
<
s
>Nam
<
lb
/>
corpus urgente hac vi centripeta revolvetur in Ellipſi immobili,
<
lb
/>
cujus centrum eſt in centro virium. </
s
>
<
s
>Quod ſi vis centripeta ſit reci
<
lb
/>
proce ut diſtantia, id eſt directe ut 1/A ſeu (A
<
emph
type
="
sup
"/>
2
<
emph.end
type
="
sup
"/>
/A
<
emph
type
="
sup
"/>
3
<
emph.end
type
="
sup
"/>
), erit
<
emph
type
="
italics
"/>
n
<
emph.end
type
="
italics
"/>
æqualis 2, ad
<
lb
/>
eoQ.E.I.ter Apſidem ſummam & imam angulus erit graduum (180/√2)
<
lb
/>
ſeu 127
<
emph
type
="
italics
"/>
gr.
<
emph.end
type
="
italics
"/>
16
<
emph
type
="
italics
"/>
m.
<
emph.end
type
="
italics
"/>
45
<
emph
type
="
italics
"/>
ſec.
<
emph.end
type
="
italics
"/>
& propterea corpus tali vi revolvens, perpe
<
lb
/>
tua anguli hujus repetitione, vicibus alternis ab Apſide ſumma ad
<
lb
/>
imam & ab ima ad ſummam perveniet in æternum. </
s
>
<
s
>Porro ſi vis
<
lb
/>
centripeta ſit reciproce ut latus quadrato-quadratum undecimæ
<
lb
/>
dignitatis altitudinis, id eſt reciproce ut A (11/4), adeoQ.E.D.recte ut
<
lb
/>
(1/A
<
emph
type
="
sup
"/>
11/4
<
emph.end
type
="
sup
"/>
) ſeu ut (A
<
emph
type
="
sup
"/>
1/4
<
emph.end
type
="
sup
"/>
/A
<
emph
type
="
sup
"/>
3
<
emph.end
type
="
sup
"/>
) erit
<
emph
type
="
italics
"/>
n
<
emph.end
type
="
italics
"/>
æqualis 1/4, & (180/√
<
emph
type
="
italics
"/>
n
<
emph.end
type
="
italics
"/>
)
<
emph
type
="
italics
"/>
gr.
<
emph.end
type
="
italics
"/>
æqualis 360
<
emph
type
="
italics
"/>
gr.
<
emph.end
type
="
italics
"/>
& prop
<
lb
/>
terea corpus de Apſide ſumma diſcedens & ſubinde perpetuo de
<
lb
/>
ſcendens, perveniet ad Apſidem imam ubi complevit revolutionem
<
lb
/>
integram, dein perpetuo aſcenſu complendo aliam revolutionem in
<
lb
/>
regram, redibit ad Apſidem ſummam: & ſic per vices in æternum. </
s
>
</
p
>
<
p
type
="
margin
">
<
s
>
<
margin.target
id
="
note104
"/>
DE MOTU
<
lb
/>
CORPORUM</
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
emph
type
="
italics
"/>
Exempl.
<
emph.end
type
="
italics
"/>
3. Aſſumentes
<
emph
type
="
italics
"/>
m
<
emph.end
type
="
italics
"/>
&
<
emph
type
="
italics
"/>
n
<
emph.end
type
="
italics
"/>
pro quibuſvis indicibus dignitatum
<
lb
/>
Altitudinis, &
<
emph
type
="
italics
"/>
b, c
<
emph.end
type
="
italics
"/>
pro numeris quibuſvis datis, ponamus vim cen
<
lb
/>
tripetam eſſe ut (
<
emph
type
="
italics
"/>
b
<
emph.end
type
="
italics
"/>
A
<
emph
type
="
sup
"/>
<
emph
type
="
italics
"/>
m
<
emph.end
type
="
italics
"/>
<
emph.end
type
="
sup
"/>
+
<
emph
type
="
italics
"/>
c
<
emph.end
type
="
italics
"/>
A
<
emph
type
="
sup
"/>
<
emph
type
="
italics
"/>
n
<
emph.end
type
="
italics
"/>
<
emph.end
type
="
sup
"/>
/A
<
emph
type
="
italics
"/>
cub.
<
emph.end
type
="
italics
"/>
), id eſt, ut (
<
emph
type
="
italics
"/>
b
<
emph.end
type
="
italics
"/>
in —T-X
<
emph
type
="
sup
"/>
<
emph
type
="
italics
"/>
m
<
emph.end
type
="
italics
"/>
<
emph.end
type
="
sup
"/>
+
<
emph
type
="
italics
"/>
c
<
emph.end
type
="
italics
"/>
in —T-X
<
emph
type
="
sup
"/>
<
emph
type
="
italics
"/>
n
<
emph.end
type
="
italics
"/>
<
emph.end
type
="
sup
"/>
/A
<
emph
type
="
italics
"/>
cub.
<
emph.end
type
="
italics
"/>
)
<
lb
/>
ſeu (per eandem Methodum noſtram Serierum convergentium) ut
<
lb
/>
(
<
emph
type
="
italics
"/>
b
<
emph.end
type
="
italics
"/>
T
<
emph
type
="
sup
"/>
<
emph
type
="
italics
"/>
m
<
emph.end
type
="
italics
"/>
<
emph.end
type
="
sup
"/>
+
<
emph
type
="
italics
"/>
c
<
emph.end
type
="
italics
"/>
T
<
emph
type
="
sup
"/>
<
emph
type
="
italics
"/>
n
<
emph.end
type
="
italics
"/>
<
emph.end
type
="
sup
"/>
-
<
emph
type
="
italics
"/>
mb
<
emph.end
type
="
italics
"/>
XT
<
emph
type
="
sup
"/>
<
emph
type
="
italics
"/>
m
<
emph.end
type
="
italics
"/>
-1
<
emph.end
type
="
sup
"/>
-
<
emph
type
="
italics
"/>
nc
<
emph.end
type
="
italics
"/>
XT
<
emph
type
="
sup
"/>
<
emph
type
="
italics
"/>
n
<
emph.end
type
="
italics
"/>
-1
<
emph.end
type
="
sup
"/>
+(
<
emph
type
="
italics
"/>
mm-mb
<
emph.end
type
="
italics
"/>
/2)XXT
<
emph
type
="
sup
"/>
<
emph
type
="
italics
"/>
m
<
emph.end
type
="
italics
"/>
-2
<
emph.end
type
="
sup
"/>
+(
<
emph
type
="
italics
"/>
nn-nc
<
emph.end
type
="
italics
"/>
/2)XXT
<
emph
type
="
sup
"/>
<
emph
type
="
italics
"/>
n
<
emph.end
type
="
italics
"/>
-2
<
emph.end
type
="
sup
"/>
<
emph
type
="
italics
"/>
&c.
<
emph.end
type
="
italics
"/>
/A
<
emph
type
="
italics
"/>
cub.
<
emph.end
type
="
italics
"/>
) </
s
>
</
p
>
</
subchap2
>
</
subchap1
>
</
chap
>
</
body
>
</
text
>
</
archimedes
>