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
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 - 800
801 - 810
811 - 820
821 - 824
>
191
(116)
192
193
194
195
(117)
196
(118)
197
(119)
198
(120)
199
(121)
200
(122)
<
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 - 800
801 - 810
811 - 820
821 - 824
>
page
|<
<
(141)
of 824
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div791
"
type
="
section
"
level
="
1
"
n
="
208
">
<
pb
o
="
141
"
file
="
0209
"
n
="
228
"
rhead
="
MATHEMATICA. LIB. I. CAP XXIII.
"/>
<
p
>
<
s
xml:id
="
echoid-s5564
"
xml:space
="
preserve
">Ex hiſce patet actione corporis hujus vim, ideoque velo-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0209-01
"
xlink:href
="
note-0209-01a
"
xml:space
="
preserve
">523.</
note
>
oitatem, non minui ſine ipſius obſtaculi, aut partium hoc
<
lb
/>
componentium; </
s
>
<
s
xml:id
="
echoid-s5565
"
xml:space
="
preserve
">translatione ex hac actione oriunda.</
s
>
<
s
xml:id
="
echoid-s5566
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div799
"
type
="
section
"
level
="
1
"
n
="
209
">
<
head
xml:id
="
echoid-head295
"
xml:space
="
preserve
">SCHOLIUM 1.</
head
>
<
head
xml:id
="
echoid-head296
"
xml:space
="
preserve
">Demonſtrationes n. 499. 510</
head
>
<
p
>
<
s
xml:id
="
echoid-s5567
"
xml:space
="
preserve
">Dentur duo corpora A & </
s
>
<
s
xml:id
="
echoid-s5568
"
xml:space
="
preserve
">B; </
s
>
<
s
xml:id
="
echoid-s5569
"
xml:space
="
preserve
">ſit hujus velocitas b; </
s
>
<
s
xml:id
="
echoid-s5570
"
xml:space
="
preserve
">illius celeritas a; </
s
>
<
s
xml:id
="
echoid-s5571
"
xml:space
="
preserve
">velo-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0209-02
"
xlink:href
="
note-0209-02a
"
xml:space
="
preserve
">524.</
note
>
citas reſpectiva, ſi in contrarias partes ferantur eſt a + b ; </
s
>
<
s
xml:id
="
echoid-s5572
"
xml:space
="
preserve
">hanc
<
note
symbol
="
*
"
position
="
right
"
xlink:label
="
note-0209-03
"
xlink:href
="
note-0209-03a
"
xml:space
="
preserve
">475.</
note
>
mus d. </
s
>
<
s
xml:id
="
echoid-s5573
"
xml:space
="
preserve
">Summa virium eſt Aaa + Bbb, quam, manente velocitate reſpecti-
<
lb
/>
va, diximus omnium minimam poſitis A, B:</
s
>
<
s
xml:id
="
echoid-s5574
"
xml:space
="
preserve
">: b, a , id eſt Aa = Bb.</
s
>
<
s
xml:id
="
echoid-s5575
"
xml:space
="
preserve
"/>
</
p
>
<
note
symbol
="
*
"
position
="
right
"
xml:space
="
preserve
">499.</
note
>
<
p
>
<
s
xml:id
="
echoid-s5576
"
xml:space
="
preserve
">Poſitis enim talibus velocitatibus, augeatur a quantitate quacunque e; </
s
>
<
s
xml:id
="
echoid-s5577
"
xml:space
="
preserve
">vis
<
lb
/>
corporis A erit nunc Aaa + 2A ae + Aee. </
s
>
<
s
xml:id
="
echoid-s5578
"
xml:space
="
preserve
">Corporis B velocitas, quia
<
lb
/>
manet velocitas reſpectiva d = a + b, erit b-e; </
s
>
<
s
xml:id
="
echoid-s5579
"
xml:space
="
preserve
">nam a + e + b - e = a + b; </
s
>
<
s
xml:id
="
echoid-s5580
"
xml:space
="
preserve
">er-
<
lb
/>
go vis corporis B erit Bbb - 2Bbe + Bee, & </
s
>
<
s
xml:id
="
echoid-s5581
"
xml:space
="
preserve
">ſumma virium eſt Aaa
<
lb
/>
+ Bbb + Aee + Bee + 2Aae - 2Bbe.</
s
>
<
s
xml:id
="
echoid-s5582
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s5583
"
xml:space
="
preserve
">Sed propter Aa = Bb ſeſe mutuo duo ultimi termini deſtruunt, & </
s
>
<
s
xml:id
="
echoid-s5584
"
xml:space
="
preserve
">ſum-
<
lb
/>
ma valet Aaa + Bbb + Aee + Bee, quæ primam excedit. </
s
>
<
s
xml:id
="
echoid-s5585
"
xml:space
="
preserve
">Similis eſt de-
<
lb
/>
monſtratio ſi augeatur velocitas b, minutâ, eâdem quantitate, velocitate a; </
s
>
<
s
xml:id
="
echoid-s5586
"
xml:space
="
preserve
">un-
<
lb
/>
de patet demonſtratio n. </
s
>
<
s
xml:id
="
echoid-s5587
"
xml:space
="
preserve
">499.</
s
>
<
s
xml:id
="
echoid-s5588
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s5589
"
xml:space
="
preserve
">Poſuimus A, B:</
s
>
<
s
xml:id
="
echoid-s5590
"
xml:space
="
preserve
">:b, a; </
s
>
<
s
xml:id
="
echoid-s5591
"
xml:space
="
preserve
">componendo A + B, B:</
s
>
<
s
xml:id
="
echoid-s5592
"
xml:space
="
preserve
">:b + a = d, a; </
s
>
<
s
xml:id
="
echoid-s5593
"
xml:space
="
preserve
">ergo
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0209-05
"
xlink:href
="
note-0209-05a
"
xml:space
="
preserve
">525.</
note
>
a = {Bd/A + B}, ſimiliter b = {Ad/A + B}; </
s
>
<
s
xml:id
="
echoid-s5594
"
xml:space
="
preserve
">idcirco ſumma virium Aaa + Bbb =
<
lb
/>
{ABBdd + BAAdd/
<
emph
style
="
ol
">B + A</
emph
>
<
emph
style
="
super
">q</
emph
>
} dividendo numeratorem & </
s
>
<
s
xml:id
="
echoid-s5595
"
xml:space
="
preserve
">denominatorem per
<
lb
/>
B + A, quantitas hæc æqualis eſt {ABdd/B + A} ut in n. </
s
>
<
s
xml:id
="
echoid-s5596
"
xml:space
="
preserve
">510. </
s
>
<
s
xml:id
="
echoid-s5597
"
xml:space
="
preserve
">monuimus.</
s
>
<
s
xml:id
="
echoid-s5598
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div802
"
type
="
section
"
level
="
1
"
n
="
210
">
<
head
xml:id
="
echoid-head297
"
style
="
it
"
xml:space
="
preserve
">Demonſtrationes Algebraicæ n. 513. 516.</
head
>
<
p
>
<
s
xml:id
="
echoid-s5599
"
xml:space
="
preserve
">Geometrice demonſtravimus regulas n. </
s
>
<
s
xml:id
="
echoid-s5600
"
xml:space
="
preserve
">513. </
s
>
<
s
xml:id
="
echoid-s5601
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s5602
"
xml:space
="
preserve
">516. </
s
>
<
s
xml:id
="
echoid-s5603
"
xml:space
="
preserve
">algebraice quam ſa-
<
lb
/>
cillime deducuntur ex propoſitione numeri 512.</
s
>
<
s
xml:id
="
echoid-s5604
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s5605
"
xml:space
="
preserve
">Sit corpus A motum velocitate a; </
s
>
<
s
xml:id
="
echoid-s5606
"
xml:space
="
preserve
">corpus B agitatum velocitate b: </
s
>
<
s
xml:id
="
echoid-s5607
"
xml:space
="
preserve
">velo-
<
lb
/>
citas reſpectiva eſt a - b ſi corpora ad eandem partem tendant ; </
s
>
<
s
xml:id
="
echoid-s5608
"
xml:space
="
preserve
">hæc ictu
<
note
position
="
right
"
xlink:label
="
note-0209-06
"
xlink:href
="
note-0209-06a
"
xml:space
="
preserve
">526.</
note
>
ſtruitur quare eſt ſumma mutationum in velocitatibus corporum poſt ictum.</
s
>
<
s
xml:id
="
echoid-s5609
"
xml:space
="
preserve
">
<
note
symbol
="
*
"
position
="
right
"
xlink:label
="
note-0209-07
"
xlink:href
="
note-0209-07a
"
xml:space
="
preserve
">474.</
note
>
B eſt ad A ut mutatio velocitatis in A, ad mutationem velocitatis in B ; </
s
>
<
s
xml:id
="
echoid-s5610
"
xml:space
="
preserve
">&</
s
>
<
s
xml:id
="
echoid-s5611
"
xml:space
="
preserve
">
<
note
symbol
="
*
"
position
="
right
"
xlink:label
="
note-0209-08
"
xlink:href
="
note-0209-08a
"
xml:space
="
preserve
">484.</
note
>
componendo A + B, A:</
s
>
<
s
xml:id
="
echoid-s5612
"
xml:space
="
preserve
">:a - b, ad mutationem in velocitate corporis B, quæ
<
lb
/>
<
note
symbol
="
*
"
position
="
right
"
xlink:label
="
note-0209-09
"
xlink:href
="
note-0209-09a
"
xml:space
="
preserve
">511.</
note
>
</
s
>
</
p
>
</
div
>
</
text
>
</
echo
>