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
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
<
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
="
039/01/169.jpg
"
pagenum
="
141
"/>
oſcillationis unius, ut arcus
<
emph
type
="
italics
"/>
HI
<
emph.end
type
="
italics
"/>
(tempus quo corpus
<
emph
type
="
italics
"/>
H
<
emph.end
type
="
italics
"/>
perveniet
<
lb
/>
<
arrow.to.target
n
="
note117
"/>
ad
<
emph
type
="
italics
"/>
L
<
emph.end
type
="
italics
"/>
) ad ſemiperipheriam
<
emph
type
="
italics
"/>
HKM
<
emph.end
type
="
italics
"/>
(tempus quo corpus
<
emph
type
="
italics
"/>
H
<
emph.end
type
="
italics
"/>
per
<
lb
/>
veniet ad
<
emph
type
="
italics
"/>
M.
<
emph.end
type
="
italics
"/>
) Et velocitas corporis penduli in loco
<
emph
type
="
italics
"/>
T
<
emph.end
type
="
italics
"/>
eſt ad ve
<
lb
/>
locitatem ipſius in loco infimo
<
emph
type
="
italics
"/>
R,
<
emph.end
type
="
italics
"/>
(hoc eſt, velocitas corporis
<
emph
type
="
italics
"/>
H
<
emph.end
type
="
italics
"/>
in
<
lb
/>
loco
<
emph
type
="
italics
"/>
L
<
emph.end
type
="
italics
"/>
ad velocitatem ejus in loco
<
emph
type
="
italics
"/>
G,
<
emph.end
type
="
italics
"/>
ſeu incrementum momenta
<
lb
/>
neum lineæ
<
emph
type
="
italics
"/>
HL
<
emph.end
type
="
italics
"/>
ad incrementum momentaneum lineæ
<
emph
type
="
italics
"/>
HG,
<
emph.end
type
="
italics
"/>
arcu
<
lb
/>
bus
<
emph
type
="
italics
"/>
HI, HK
<
emph.end
type
="
italics
"/>
æquabili fluxu creſcentibus) ut ordinatim applicata
<
lb
/>
<
emph
type
="
italics
"/>
LI
<
emph.end
type
="
italics
"/>
ad radium
<
emph
type
="
italics
"/>
GK,
<
emph.end
type
="
italics
"/>
ſive ut √
<
emph
type
="
italics
"/>
<
expan
abbr
="
SRq.-TRq.
">SRq.-TRque</
expan
>
<
emph.end
type
="
italics
"/>
ad
<
emph
type
="
italics
"/>
SR.
<
emph.end
type
="
italics
"/>
Unde cum,
<
lb
/>
in oſcillationibus inæqualibus, deſcribantur æqualibus temporibus
<
lb
/>
arcus totis oſcillationum arcubus proportionales; habentur, ex da
<
lb
/>
tis temporibus, & velocitates & arcus deſcripti in oſcillationibus
<
lb
/>
univerſis. </
s
>
<
s
>Quæ erant primo invenienda. </
s
>
</
p
>
<
p
type
="
margin
">
<
s
>
<
margin.target
id
="
note117
"/>
LIBER
<
lb
/>
PRIMUS.</
s
>
</
p
>
<
p
type
="
main
">
<
s
>Oſcillentur jam Funipendula
<
lb
/>
<
figure
id
="
id.039.01.169.1.jpg
"
xlink:href
="
039/01/169/1.jpg
"
number
="
100
"/>
<
lb
/>
corpora in Cycloidibus diverſis
<
lb
/>
intra Globos diverſos, quorum
<
lb
/>
diverſæ ſunt etiam Vires abſolu
<
lb
/>
tæ, deſcriptis: &, ſi Vis abſolu
<
lb
/>
ta Globi cujuſvis
<
emph
type
="
italics
"/>
QOS
<
emph.end
type
="
italics
"/>
dicatur V,
<
lb
/>
Vis acceleratrix qua
<
expan
abbr
="
Pendulũ
">Pendulum</
expan
>
urge
<
lb
/>
tur in circumferentia hujus Globi,
<
lb
/>
ubi incipit directe verſus centrum
<
lb
/>
ejus moveri, erit ut diſtantia Cor
<
lb
/>
poris penduli a centro illo & Vis abſoluta Globi conjunctim, hoc
<
lb
/>
eſt, ut
<
emph
type
="
italics
"/>
CO
<
emph.end
type
="
italics
"/>
XV. </
s
>
<
s
>Itaque lineola
<
emph
type
="
italics
"/>
HY,
<
emph.end
type
="
italics
"/>
quæ ſit ut hæc Vis accelera
<
lb
/>
trix
<
emph
type
="
italics
"/>
CO
<
emph.end
type
="
italics
"/>
XV, deſcribetur dato tempore; &, ſi erigatur normalis
<
emph
type
="
italics
"/>
YZ
<
emph.end
type
="
italics
"/>
<
lb
/>
circumferentiæ occurrens in
<
emph
type
="
italics
"/>
Z,
<
emph.end
type
="
italics
"/>
arcus naſcens
<
emph
type
="
italics
"/>
HZ
<
emph.end
type
="
italics
"/>
denotabit datum
<
lb
/>
illud tempus. </
s
>
<
s
>Eſt autem arcus hic naſcens
<
emph
type
="
italics
"/>
HZ
<
emph.end
type
="
italics
"/>
in ſubduplicata ra
<
lb
/>
tione rectanguli
<
emph
type
="
italics
"/>
GHY,
<
emph.end
type
="
italics
"/>
adeoque ut √
<
emph
type
="
italics
"/>
GHXCO
<
emph.end
type
="
italics
"/>
XV. </
s
>
<
s
>Unde Tem
<
lb
/>
pus oſcillationis integræ in Cycloide
<
emph
type
="
italics
"/>
QRS
<
emph.end
type
="
italics
"/>
(cum ſit ut ſemiperi
<
lb
/>
pheria
<
emph
type
="
italics
"/>
HKM,
<
emph.end
type
="
italics
"/>
quæ oſcillationem illam integram denotat, directe,
<
lb
/>
utque arcus
<
emph
type
="
italics
"/>
HZ,
<
emph.end
type
="
italics
"/>
qui datum tempus ſimiliter denotat, inverſe) fiet
<
lb
/>
ut
<
emph
type
="
italics
"/>
GH
<
emph.end
type
="
italics
"/>
directe & √
<
emph
type
="
italics
"/>
GHXCO
<
emph.end
type
="
italics
"/>
XV inverſe, hoc eſt, ob æquales
<
emph
type
="
italics
"/>
GH
<
emph.end
type
="
italics
"/>
<
lb
/>
&
<
emph
type
="
italics
"/>
SR,
<
emph.end
type
="
italics
"/>
ut √(
<
emph
type
="
italics
"/>
SR/CO
<
emph.end
type
="
italics
"/>
XV), ſive (per Corol. </
s
>
<
s
>Prop. </
s
>
<
s
>L) ut √(
<
emph
type
="
italics
"/>
AR/AC
<
emph.end
type
="
italics
"/>
XV).
<
lb
/>
Itaque Oſcillationes in Globis & Cycloidibus omnibus, quibuſ
<
lb
/>
cunque cum Viribus abſolutis factæ, ſunt in ratione quæ compo
<
lb
/>
nitur ex ſubduplicata ratione longitudinis Fili directe, & ſubdu
<
lb
/>
plicata ratione diſtantiæ inter punctum ſuſpenſionis & centrum </
s
>
</
p
>
</
subchap2
>
</
subchap1
>
</
chap
>
</
body
>
</
text
>
</
archimedes
>