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
List of thumbnails
<
1 - 10
11 - 20
21 - 30
31 - 40
41 - 50
51 - 60
61 - 70
71 - 80
81 - 90
91 - 100
101 - 110
111 - 120
121 - 130
131 - 140
141 - 150
151 - 160
161 - 170
171 - 180
181 - 190
191 - 200
201 - 210
211 - 220
221 - 230
231 - 240
241 - 250
251 - 260
261 - 270
271 - 280
281 - 290
291 - 300
301 - 310
311 - 320
321 - 330
331 - 340
341 - 350
351 - 360
361 - 370
371 - 380
381 - 390
391 - 400
401 - 410
411 - 420
421 - 430
431 - 440
441 - 450
451 - 460
461 - 470
471 - 480
481 - 490
491 - 500
501 - 510
511 - 520
521 - 530
531 - 540
541 - 550
551 - 560
561 - 570
571 - 580
581 - 590
591 - 600
601 - 610
611 - 620
621 - 630
631 - 640
641 - 650
651 - 660
661 - 670
671 - 680
681 - 690
691 - 700
701 - 710
711 - 720
721 - 730
731 - 740
741 - 750
751 - 760
761 - 770
771 - 780
781 - 790
791 - 795
>
531
(517)
532
(518)
533
(519)
534
(520)
535
(521)
536
(522)
537
(523)
538
(524)
539
(525)
540
(526)
<
1 - 10
11 - 20
21 - 30
31 - 40
41 - 50
51 - 60
61 - 70
71 - 80
81 - 90
91 - 100
101 - 110
111 - 120
121 - 130
131 - 140
141 - 150
151 - 160
161 - 170
171 - 180
181 - 190
191 - 200
201 - 210
211 - 220
221 - 230
231 - 240
241 - 250
251 - 260
261 - 270
271 - 280
281 - 290
291 - 300
301 - 310
311 - 320
321 - 330
331 - 340
341 - 350
351 - 360
361 - 370
371 - 380
381 - 390
391 - 400
401 - 410
411 - 420
421 - 430
431 - 440
441 - 450
451 - 460
461 - 470
471 - 480
481 - 490
491 - 500
501 - 510
511 - 520
521 - 530
531 - 540
541 - 550
551 - 560
561 - 570
571 - 580
581 - 590
591 - 600
601 - 610
611 - 620
621 - 630
631 - 640
641 - 650
651 - 660
661 - 670
671 - 680
681 - 690
691 - 700
701 - 710
711 - 720
721 - 730
731 - 740
741 - 750
751 - 760
761 - 770
771 - 780
781 - 790
791 - 795
>
page
|<
<
(597)
of 795
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div552
"
type
="
section
"
level
="
1
"
n
="
552
">
<
p
>
<
s
xml:id
="
echoid-s14773
"
xml:space
="
preserve
">
<
pb
o
="
597
"
file
="
0613
"
n
="
614
"
rhead
="
CORPORUM FIRMORUM.
"/>
tas parabolæ, dabit {2/15} a a c r. </
s
>
<
s
xml:id
="
echoid-s14774
"
xml:space
="
preserve
">eodem modo reperitur momentum
<
lb
/>
ſegmenti D B E = {2a a c b
<
emph
style
="
super
">10</
emph
>
/15 r
<
emph
style
="
super
">9</
emph
>
}. </
s
>
<
s
xml:id
="
echoid-s14775
"
xml:space
="
preserve
">Eſt autem Cohærentia baſeos Parabo-
<
lb
/>
læ A B C = 8r
<
emph
style
="
super
">3</
emph
>
. </
s
>
<
s
xml:id
="
echoid-s14776
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s14777
"
xml:space
="
preserve
">Cohærentia baſeos D G E = 8b3. </
s
>
<
s
xml:id
="
echoid-s14778
"
xml:space
="
preserve
">quare momen-
<
lb
/>
tum Parabolæ A B C, ad ſuam Cohærentiam eſt, ut {2/15} a a c r ad 8r3.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s14779
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s14780
"
xml:space
="
preserve
">momentum ſegmenti D B E ad ſuam Cohærentiam, uti {2a a c b
<
emph
style
="
super
">10</
emph
>
/15 r
<
emph
style
="
super
">9</
emph
>
.</
s
>
<
s
xml:id
="
echoid-s14781
"
xml:space
="
preserve
">}
<
lb
/>
ad 8b
<
emph
style
="
super
">3</
emph
>
.</
s
>
<
s
xml:id
="
echoid-s14782
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s14783
"
xml:space
="
preserve
">Corol. </
s
>
<
s
xml:id
="
echoid-s14784
"
xml:space
="
preserve
">1. </
s
>
<
s
xml:id
="
echoid-s14785
"
xml:space
="
preserve
">Ergo ſolidi Parabolici A B C, Cohærentia ad ſuum momen-
<
lb
/>
tum ex gravitate eſt in minori ratione, quam Cohærentia ſegmenti
<
lb
/>
D B E ad ſuum momentum. </
s
>
<
s
xml:id
="
echoid-s14786
"
xml:space
="
preserve
">Nam Cohærentia A B C ad ſuum mo-
<
lb
/>
mentum eſt ut r
<
emph
style
="
super
">3</
emph
>
ad {2/15} a a c r. </
s
>
<
s
xml:id
="
echoid-s14787
"
xml:space
="
preserve
">ſive ut r
<
emph
style
="
super
">9</
emph
>
ad {2/15} a a c r
<
emph
style
="
super
">7</
emph
>
. </
s
>
<
s
xml:id
="
echoid-s14788
"
xml:space
="
preserve
">eſt Cohæren-
<
lb
/>
tia ſegmenti D B E ad ſuum momentum uti b3 ad {2 a a c b
<
emph
style
="
super
">10</
emph
>
/15 r
<
emph
style
="
super
">9</
emph
>
.</
s
>
<
s
xml:id
="
echoid-s14789
"
xml:space
="
preserve
">} ſive uti
<
lb
/>
r9 ad {2/15} a a c b
<
emph
style
="
super
">7</
emph
>
. </
s
>
<
s
xml:id
="
echoid-s14790
"
xml:space
="
preserve
">quia autem r eſt major quam b. </
s
>
<
s
xml:id
="
echoid-s14791
"
xml:space
="
preserve
">erit ratio r
<
emph
style
="
super
">9</
emph
>
ad {2/15}
<
lb
/>
a a c r
<
emph
style
="
super
">7</
emph
>
minor quam r
<
emph
style
="
super
">9</
emph
>
, ad {2/15} a a c b7.</
s
>
<
s
xml:id
="
echoid-s14792
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s14793
"
xml:space
="
preserve
">Corol. </
s
>
<
s
xml:id
="
echoid-s14794
"
xml:space
="
preserve
">2. </
s
>
<
s
xml:id
="
echoid-s14795
"
xml:space
="
preserve
">Ergo majus pondus poterit vertici B ſegmenti D B E
<
lb
/>
appendi, quam paraboloidis A B C.</
s
>
<
s
xml:id
="
echoid-s14796
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div553
"
type
="
section
"
level
="
1
"
n
="
553
">
<
head
xml:id
="
echoid-head667
"
xml:space
="
preserve
">PROPOSITIO LXXIV.</
head
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s14797
"
xml:space
="
preserve
">Tab. </
s
>
<
s
xml:id
="
echoid-s14798
"
xml:space
="
preserve
">XXVI. </
s
>
<
s
xml:id
="
echoid-s14799
"
xml:space
="
preserve
">fig. </
s
>
<
s
xml:id
="
echoid-s14800
"
xml:space
="
preserve
">1. </
s
>
<
s
xml:id
="
echoid-s14801
"
xml:space
="
preserve
">Dato ſegmento præcedentis Paraboloidis
<
lb
/>
D B E gravi, atque pondere P maximo, quod geſtari poſſit, inve-
<
lb
/>
nire pondus ex vertice B Parabolæ A B C geſtandum.</
s
>
<
s
xml:id
="
echoid-s14802
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s14803
"
xml:space
="
preserve
">Quantitatibus deſignatis ut ante, & </
s
>
<
s
xml:id
="
echoid-s14804
"
xml:space
="
preserve
">pondere P vocato = p. </
s
>
<
s
xml:id
="
echoid-s14805
"
xml:space
="
preserve
">quæ-
<
lb
/>
ſito = x. </
s
>
<
s
xml:id
="
echoid-s14806
"
xml:space
="
preserve
">ordinanda erit hæc proportio {2 a a c b
<
emph
style
="
super
">10</
emph
>
/15 r
<
emph
style
="
super
">9</
emph
>
} + {a b
<
emph
style
="
super
">4</
emph
>
p. </
s
>
<
s
xml:id
="
echoid-s14807
"
xml:space
="
preserve
">8 b
<
emph
style
="
super
">3</
emph
>
:</
s
>
<
s
xml:id
="
echoid-s14808
"
xml:space
="
preserve
">:/r
<
emph
style
="
super
">4</
emph
>
}
<
lb
/>
{2/15} a a c r + a x. </
s
>
<
s
xml:id
="
echoid-s14809
"
xml:space
="
preserve
">8r
<
emph
style
="
super
">3</
emph
>
. </
s
>
<
s
xml:id
="
echoid-s14810
"
xml:space
="
preserve
">ex quibus eruitur x = {2 a c b 7/15 r
<
emph
style
="
super
">6</
emph
>
} + {b p/r}-{2/15
<
unsure
/>
} a c r.</
s
>
<
s
xml:id
="
echoid-s14811
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div554
"
type
="
section
"
level
="
1
"
n
="
554
">
<
head
xml:id
="
echoid-head668
"
xml:space
="
preserve
">PROPOSITIO LXXV.</
head
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s14812
"
xml:space
="
preserve
">Tab. </
s
>
<
s
xml:id
="
echoid-s14813
"
xml:space
="
preserve
">XXVI. </
s
>
<
s
xml:id
="
echoid-s14814
"
xml:space
="
preserve
">Fig. </
s
>
<
s
xml:id
="
echoid-s14815
"
xml:space
="
preserve
">3. </
s
>
<
s
xml:id
="
echoid-s14816
"
xml:space
="
preserve
">Sit Parabola Apolloniana A D B, cujus
<
lb
/>
Tangens ſit T A, ducta ſit T B parallela ad A D, circa A T veluti
<
lb
/>
axin & </
s
>
<
s
xml:id
="
echoid-s14817
"
xml:space
="
preserve
">radio T B circumagatur Parabola, deſcribetur corpus pa-
<
lb
/>
raboliforme A C B A fig. </
s
>
<
s
xml:id
="
echoid-s14818
"
xml:space
="
preserve
">4. </
s
>
<
s
xml:id
="
echoid-s14819
"
xml:space
="
preserve
">cujus baſis eſt C T B, dico hoc </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>