Musschenbroek, Petrus van
,
Physicae experimentales, et geometricae de magnete, tuborum capillarium vitreorumque speculorum attractione, magnitudine terrae, cohaerentia corporum firmorum dissertationes: ut et ephemerides meteorologicae ultraiectinae
Text
Text Image
Image
XML
Thumbnail overview
Document information
None
Concordance
Notes
Handwritten
Figures
Content
Thumbnails
Table of Notes
<
1 - 2
[out of range]
>
<
1 - 2
[out of range]
>
page
|<
<
(549)
of 795
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div495
"
type
="
section
"
level
="
1
"
n
="
495
">
<
p
style
="
it
">
<
s
xml:id
="
echoid-s12956
"
xml:space
="
preserve
">
<
pb
o
="
549
"
file
="
0565
"
n
="
566
"
rhead
="
CORPORUM FIRMORUM.
"/>
atque Potentia frangens extremitati D applicata agat directione
<
lb
/>
ad horizontem perpendiculari, fiet ruptura in orâ foraminis A E F.</
s
>
<
s
xml:id
="
echoid-s12957
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s12958
"
xml:space
="
preserve
">Poteſt conſiderari longitudo corporis A D ut vectis, cujus ful-
<
lb
/>
crum eſt ad A, potentia in D, eligatur quæcunque ſectio intermedia
<
lb
/>
C parallelela baſi A E F, in hac C, erit Cohærentia eadem ac in baſi
<
lb
/>
A E F, quia corpus eſt ubique æque craſſum: </
s
>
<
s
xml:id
="
echoid-s12959
"
xml:space
="
preserve
">eſt vero momentum po-
<
lb
/>
tentiæ D majus, applicatum vecti A D, quam D C breviori; </
s
>
<
s
xml:id
="
echoid-s12960
"
xml:space
="
preserve
">adeoque
<
lb
/>
potius ſuperabitur Cohærentia in A E F quam in C, & </
s
>
<
s
xml:id
="
echoid-s12961
"
xml:space
="
preserve
">quia vectis
<
lb
/>
A D eſt longiſſimus omnium in latere A D, cujus ope potentia maxi-
<
lb
/>
mum momentum exercet, franget hæc corpus in ora foraminis A E F.</
s
>
<
s
xml:id
="
echoid-s12962
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div496
"
type
="
section
"
level
="
1
"
n
="
496
">
<
head
xml:id
="
echoid-head608
"
xml:space
="
preserve
">PROPOSITIO XX.</
head
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s12963
"
xml:space
="
preserve
">Tab. </
s
>
<
s
xml:id
="
echoid-s12964
"
xml:space
="
preserve
">XIX. </
s
>
<
s
xml:id
="
echoid-s12965
"
xml:space
="
preserve
">fig. </
s
>
<
s
xml:id
="
echoid-s12966
"
xml:space
="
preserve
">3. </
s
>
<
s
xml:id
="
echoid-s12967
"
xml:space
="
preserve
">Si dentur duo parallelopipeda horizontalia F E
<
lb
/>
A C, F E A D, ejusdem materiæ & </
s
>
<
s
xml:id
="
echoid-s12968
"
xml:space
="
preserve
">craſſitiei, ſed diverſæ longitu-
<
lb
/>
dinis A C, A D, quorum extremitatibus C & </
s
>
<
s
xml:id
="
echoid-s12969
"
xml:space
="
preserve
">D applicentur Po-
<
lb
/>
tentiæ rumpentes, harumque directiones ſint perpendiculares in A C
<
lb
/>
& </
s
>
<
s
xml:id
="
echoid-s12970
"
xml:space
="
preserve
">A D, ſepoſitâ corporum gravitate requirentur potentiæ ad C
<
lb
/>
& </
s
>
<
s
xml:id
="
echoid-s12971
"
xml:space
="
preserve
">D in ratione reciprocâ longitudinum A C, A D.</
s
>
<
s
xml:id
="
echoid-s12972
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s12973
"
xml:space
="
preserve
">Quando franguntur hæc parallelopipeda in EAF primo ſolvun-
<
lb
/>
tur partes ſuperiores E, tum quæ propiores ſunt ad A, fitque ro-
<
lb
/>
tatio circa infimum punctum A, adeoque E A C, E A D poſſunt
<
lb
/>
conſiderari ut duo vectes incurvi, quorum centrum motus eſt in A,
<
lb
/>
& </
s
>
<
s
xml:id
="
echoid-s12974
"
xml:space
="
preserve
">qui brachia habent EA, AC, tum EA, AD: </
s
>
<
s
xml:id
="
echoid-s12975
"
xml:space
="
preserve
">Eſt autem Cohæ-
<
lb
/>
rentia baſium EAF eadem, quia ſunt baſes eædem, adeoque earum
<
lb
/>
reſiſtentia eſt eadem; </
s
>
<
s
xml:id
="
echoid-s12976
"
xml:space
="
preserve
">ſed reſiſtentia totius lateris A E poteſt conſi-
<
lb
/>
derari inſtar ponderis vel potentiæ applicatæ puncto E vectis E A:
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s12977
"
xml:space
="
preserve
">Eſt igitur potentia requiſita in C ad pondus vel potentiam in E, uti
<
lb
/>
E A ad A C: </
s
>
<
s
xml:id
="
echoid-s12978
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s12979
"
xml:space
="
preserve
">potentia in D, ad idem pondus vel potentiam E,
<
lb
/>
uti EA ad AD. </
s
>
<
s
xml:id
="
echoid-s12980
"
xml:space
="
preserve
">quia EA eſt eadem quantitas poteſt poni = 1. </
s
>
<
s
xml:id
="
echoid-s12981
"
xml:space
="
preserve
">hinc
<
lb
/>
ſtabit C. </
s
>
<
s
xml:id
="
echoid-s12982
"
xml:space
="
preserve
">E:</
s
>
<
s
xml:id
="
echoid-s12983
"
xml:space
="
preserve
">: 1. </
s
>
<
s
xml:id
="
echoid-s12984
"
xml:space
="
preserve
">AC. </
s
>
<
s
xml:id
="
echoid-s12985
"
xml:space
="
preserve
">ſive {C/E}:</
s
>
<
s
xml:id
="
echoid-s12986
"
xml:space
="
preserve
">: {1.</
s
>
<
s
xml:id
="
echoid-s12987
"
xml:space
="
preserve
">/AC} tum D.</
s
>
<
s
xml:id
="
echoid-s12988
"
xml:space
="
preserve
">E:</
s
>
<
s
xml:id
="
echoid-s12989
"
xml:space
="
preserve
">: 1. </
s
>
<
s
xml:id
="
echoid-s12990
"
xml:space
="
preserve
">AD. </
s
>
<
s
xml:id
="
echoid-s12991
"
xml:space
="
preserve
">ſive {D/E}:</
s
>
<
s
xml:id
="
echoid-s12992
"
xml:space
="
preserve
">:
<
lb
/>
{1.</
s
>
<
s
xml:id
="
echoid-s12993
"
xml:space
="
preserve
">/AD} ſed eſt {C/E} ad {D/E}:</
s
>
<
s
xml:id
="
echoid-s12994
"
xml:space
="
preserve
">: C.</
s
>
<
s
xml:id
="
echoid-s12995
"
xml:space
="
preserve
">D. </
s
>
<
s
xml:id
="
echoid-s12996
"
xml:space
="
preserve
">quare C.</
s
>
<
s
xml:id
="
echoid-s12997
"
xml:space
="
preserve
">D:</
s
>
<
s
xml:id
="
echoid-s12998
"
xml:space
="
preserve
">: {1.</
s
>
<
s
xml:id
="
echoid-s12999
"
xml:space
="
preserve
">/AC} {1.</
s
>
<
s
xml:id
="
echoid-s13000
"
xml:space
="
preserve
">/AD}:</
s
>
<
s
xml:id
="
echoid-s13001
"
xml:space
="
preserve
">: AD. </
s
>
<
s
xml:id
="
echoid-s13002
"
xml:space
="
preserve
">AC
<
lb
/>
hoc eſt, erit C ad D in ratione reciproca longitudinum AC ad AD.</
s
>
<
s
xml:id
="
echoid-s13003
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s13004
"
xml:space
="
preserve
">Hac propoſitione uſus fui in Experimentis præcedentibus, </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>