Gravesande, Willem Jacob 's
,
Physices elementa mathematica, experimentis confirmata sive introductio ad philosophiam Newtonianam; Tom. 1
Text
Text Image
Image
XML
Thumbnail overview
Document information
None
Concordance
Notes
Handwritten
Figures
Content
Thumbnails
page
|<
<
(53)
of 824
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div375
"
type
="
section
"
level
="
1
"
n
="
127
">
<
p
>
<
s
xml:id
="
echoid-s2355
"
xml:space
="
preserve
">
<
pb
o
="
53
"
file
="
0099
"
n
="
107
"
rhead
="
MATHEMATICA. LIB. I. CAP. XV.
"/>
rum directiones ſunt parallelæ lateribus trianguli AED; </
s
>
<
s
xml:id
="
echoid-s2356
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s2357
"
xml:space
="
preserve
">
<
lb
/>
quæ ergo, ut detur æquilibrium, ſunt inter ſe ut iſta latera.</
s
>
<
s
xml:id
="
echoid-s2358
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s2359
"
xml:space
="
preserve
">Punctum A, ob æqualitatem diſtantiarum punctorum A
<
lb
/>
& </
s
>
<
s
xml:id
="
echoid-s2360
"
xml:space
="
preserve
">B a fulcro, juxta
<
emph
style
="
sc
">Ea</
emph
>
continuatam, trahitur eadem vi
<
lb
/>
qua pondus P deſcendit, id eſt, pondere duarum librarum;
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s2361
"
xml:space
="
preserve
">vis ergo per AD requiritur trium librarum, quia latera AD
<
lb
/>
& </
s
>
<
s
xml:id
="
echoid-s2362
"
xml:space
="
preserve
">AE ſunt inter ſe ut tria ad duo. </
s
>
<
s
xml:id
="
echoid-s2363
"
xml:space
="
preserve
">Latus DE exprimit
<
lb
/>
quid fulcrum patiatur vi qua punctum A in fig. </
s
>
<
s
xml:id
="
echoid-s2364
"
xml:space
="
preserve
">2. </
s
>
<
s
xml:id
="
echoid-s2365
"
xml:space
="
preserve
">premitur
<
lb
/>
B verſus, & </
s
>
<
s
xml:id
="
echoid-s2366
"
xml:space
="
preserve
">in fig. </
s
>
<
s
xml:id
="
echoid-s2367
"
xml:space
="
preserve
">3. </
s
>
<
s
xml:id
="
echoid-s2368
"
xml:space
="
preserve
">à B retrahitur.</
s
>
<
s
xml:id
="
echoid-s2369
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s2370
"
xml:space
="
preserve
">Idem omnino dicendum de potentia obliqua axi in peri-
<
lb
/>
trochio applicata.</
s
>
<
s
xml:id
="
echoid-s2371
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div378
"
type
="
section
"
level
="
1
"
n
="
128
">
<
head
xml:id
="
echoid-head185
"
xml:space
="
preserve
">
<
emph
style
="
sc
">Experimentum</
emph
>
5.</
head
>
<
p
>
<
s
xml:id
="
echoid-s2372
"
xml:space
="
preserve
">Pondus P, trochleæ annexum, ſuſtinetur potentiis ab u-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0099-01
"
xlink:href
="
note-0099-01a
"
xml:space
="
preserve
">232.</
note
>
traque parte funi ductario applicatis, ſed oblique trahenti-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0099-02
"
xlink:href
="
note-0099-02a
"
xml:space
="
preserve
">TAB. IX.
<
lb
/>
fig. 4.</
note
>
bus per CA & </
s
>
<
s
xml:id
="
echoid-s2373
"
xml:space
="
preserve
">CB; </
s
>
<
s
xml:id
="
echoid-s2374
"
xml:space
="
preserve
">hæ potentiæ ſunt æquales inter ſe, quia
<
lb
/>
omnis funis trochleam circumdans non quieſcit, niſi ab u-
<
lb
/>
traque parte æqualiter trahatur ; </
s
>
<
s
xml:id
="
echoid-s2375
"
xml:space
="
preserve
">ipſum pondus P eſt
<
note
symbol
="
*
"
position
="
right
"
xlink:label
="
note-0099-03
"
xlink:href
="
note-0099-03a
"
xml:space
="
preserve
">124.</
note
>
ſi tertia potentia, & </
s
>
<
s
xml:id
="
echoid-s2376
"
xml:space
="
preserve
">ita punctum C tribus potentiis trahi-
<
lb
/>
tur. </
s
>
<
s
xml:id
="
echoid-s2377
"
xml:space
="
preserve
">Concipiatur linea CE ad horizontem perpendicularis,
<
lb
/>
& </
s
>
<
s
xml:id
="
echoid-s2378
"
xml:space
="
preserve
">linea AE parallela lineæ CB: </
s
>
<
s
xml:id
="
echoid-s2379
"
xml:space
="
preserve
">ſi CE ſit ad AE aut AC,
<
lb
/>
(hæ enim duæ lineæ ſunt æquales, propter memoratam æ-
<
lb
/>
qualitatem potentiarum trahentium per CB, CA ,)
<
note
symbol
="
*
"
position
="
right
"
xlink:label
="
note-0099-04
"
xlink:href
="
note-0099-04a
"
xml:space
="
preserve
">220.</
note
>
ſex ad quinque, pondus P ſex librarum a ponderibus Q & </
s
>
<
s
xml:id
="
echoid-s2380
"
xml:space
="
preserve
">
<
lb
/>
Q quinque librarum ſuſtinetur; </
s
>
<
s
xml:id
="
echoid-s2381
"
xml:space
="
preserve
">cujus ratio patet ex n. </
s
>
<
s
xml:id
="
echoid-s2382
"
xml:space
="
preserve
">220.</
s
>
<
s
xml:id
="
echoid-s2383
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s2384
"
xml:space
="
preserve
">Si extremitas una funis ductarii annectatur clavo, unico
<
lb
/>
pondere ut Q, pondus P ſuſtinetur.</
s
>
<
s
xml:id
="
echoid-s2385
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div380
"
type
="
section
"
level
="
1
"
n
="
129
">
<
head
xml:id
="
echoid-head186
"
xml:space
="
preserve
">
<
emph
style
="
sc
">Experimentum</
emph
>
6.</
head
>
<
p
>
<
s
xml:id
="
echoid-s2386
"
xml:space
="
preserve
">Si pondus P Trochleæ non conjungatur, ſed funibus
<
emph
style
="
sc
">Ca</
emph
>
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0099-05
"
xlink:href
="
note-0099-05a
"
xml:space
="
preserve
">233.</
note
>
& </
s
>
<
s
xml:id
="
echoid-s2387
"
xml:space
="
preserve
">CB, ei annexis, ſuſtineatur, poterit ſuſtineri poten-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0099-06
"
xlink:href
="
note-0099-06a
"
xml:space
="
preserve
">TAB. IX.
<
lb
/>
fig. 5.</
note
>
tiis duabus inæqualibus; </
s
>
<
s
xml:id
="
echoid-s2388
"
xml:space
="
preserve
">formetur ut in Experimento præ-
<
lb
/>
cedenti triangulum
<
emph
style
="
sc
">Ca</
emph
>
E, & </
s
>
<
s
xml:id
="
echoid-s2389
"
xml:space
="
preserve
">ſit AE undecim,
<
emph
style
="
sc
">Ca</
emph
>
duo-
<
lb
/>
decim cum ſemiſſe, & </
s
>
<
s
xml:id
="
echoid-s2390
"
xml:space
="
preserve
">CE duodecim; </
s
>
<
s
xml:id
="
echoid-s2391
"
xml:space
="
preserve
">dabitur æquilibri-
<
lb
/>
um, ſi pondera Q & </
s
>
<
s
xml:id
="
echoid-s2392
"
xml:space
="
preserve
">Q ſint ad P ut primi numeri ad ulti-
<
lb
/>
mum; </
s
>
<
s
xml:id
="
echoid-s2393
"
xml:space
="
preserve
">cujus Experimenti ratio iterum patet ex n. </
s
>
<
s
xml:id
="
echoid-s2394
"
xml:space
="
preserve
">220.</
s
>
<
s
xml:id
="
echoid-s2395
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s2396
"
xml:space
="
preserve
">Hic in tranſitu obſervandum, ex datis inclinationibus fi-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0099-07
"
xlink:href
="
note-0099-07a
"
xml:space
="
preserve
">234.</
note
>
lorum
<
emph
style
="
sc
">Ca</
emph
>
& </
s
>
<
s
xml:id
="
echoid-s2397
"
xml:space
="
preserve
">CB ad horizontem, proportionem </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>