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
>
131
(71)
132
(72)
133
134
135
136
(73)
137
(74)
138
(75)
139
(76)
140
(77)
<
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
|<
<
(73)
of 824
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div474
"
type
="
section
"
level
="
1
"
n
="
155
">
<
p
>
<
s
xml:id
="
echoid-s3033
"
xml:space
="
preserve
">
<
pb
o
="
73
"
file
="
0125
"
n
="
136
"
rhead
="
MATHEMATICA. LIB. I. CAP. XIX.
"/>
dem tempore corpus hoc percurreret Eb & </
s
>
<
s
xml:id
="
echoid-s3034
"
xml:space
="
preserve
">quæ exprimitur per Q x E b .</
s
>
<
s
xml:id
="
echoid-s3035
"
xml:space
="
preserve
">
<
note
symbol
="
*
"
position
="
right
"
xlink:label
="
note-0125-01
"
xlink:href
="
note-0125-01a
"
xml:space
="
preserve
">108.</
note
>
Potentia autem, quæ in P agit, augetur quantitate, qua P eodem tempore
<
lb
/>
transfertur per aD, & </
s
>
<
s
xml:id
="
echoid-s3036
"
xml:space
="
preserve
">quæ exprimitur per P x a D ; </
s
>
<
s
xml:id
="
echoid-s3037
"
xml:space
="
preserve
">ponimus enim
<
note
symbol
="
*
"
position
="
right
"
xlink:label
="
note-0125-02
"
xlink:href
="
note-0125-02a
"
xml:space
="
preserve
">128.</
note
>
rallelas Bb, Oo, Aa; </
s
>
<
s
xml:id
="
echoid-s3038
"
xml:space
="
preserve
">potentia ergo quæ retardat motum corporis Q, eſt ad
<
lb
/>
potentiam, quæ accelerat motum corporis P, ut Q x E b ad P x a D: </
s
>
<
s
xml:id
="
echoid-s3039
"
xml:space
="
preserve
">Sed po-
<
lb
/>
tentiæ hæapplicantur vecti, cujusfulcrum eſt C; </
s
>
<
s
xml:id
="
echoid-s3040
"
xml:space
="
preserve
">idcirco harum actiones, quas
<
lb
/>
æquales demonſtravimus, ſunt ut CB x E b x Q ad CA x a D x P . </
s
>
<
s
xml:id
="
echoid-s3041
"
xml:space
="
preserve
">Ideo CB x
<
note
symbol
="
*
"
position
="
right
"
xlink:label
="
note-0125-03
"
xlink:href
="
note-0125-03a
"
xml:space
="
preserve
">175.</
note
>
ad CA x P, ut aD ad Eb, aut AO ad OB. </
s
>
<
s
xml:id
="
echoid-s3042
"
xml:space
="
preserve
">Q. </
s
>
<
s
xml:id
="
echoid-s3043
"
xml:space
="
preserve
">E. </
s
>
<
s
xml:id
="
echoid-s3044
"
xml:space
="
preserve
">D. </
s
>
<
s
xml:id
="
echoid-s3045
"
xml:space
="
preserve
">Patet etiam in pendu-
<
lb
/>
lo tali compoſito producta fore æqualia, ſi unumquodque pondus multipli-
<
lb
/>
cetur per ſuas diſtantias a centris ſuſpenſionis & </
s
>
<
s
xml:id
="
echoid-s3046
"
xml:space
="
preserve
">oſcillationis.</
s
>
<
s
xml:id
="
echoid-s3047
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s3048
"
xml:space
="
preserve
">Si plura pondera dentur & </
s
>
<
s
xml:id
="
echoid-s3049
"
xml:space
="
preserve
">unumquodque per ſuas diſtantias a centris ſuſpenſio-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0125-04
"
xlink:href
="
note-0125-04a
"
xml:space
="
preserve
">309.</
note
>
nis & </
s
>
<
s
xml:id
="
echoid-s3050
"
xml:space
="
preserve
">oſcillationis multiplicetur, ſummæ productorum ab utraque parte centri o-
<
lb
/>
ſcillationis æquales ſunt. </
s
>
<
s
xml:id
="
echoid-s3051
"
xml:space
="
preserve
">Quod demonſtratione ſimili evincitur.</
s
>
<
s
xml:id
="
echoid-s3052
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s3053
"
xml:space
="
preserve
">Unde deducimus Methodum computatione determinandi centrum oſcil-
<
lb
/>
lationis.</
s
>
<
s
xml:id
="
echoid-s3054
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s3055
"
xml:space
="
preserve
">Sint corpora quæcunque A, B, C, D, E, horum diſtantiæ a centro ſuſpen-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0125-05
"
xlink:href
="
note-0125-05a
"
xml:space
="
preserve
">310.</
note
>
ſionis reſpectivè litteris a, b, c, d, e, exprimuntur; </
s
>
<
s
xml:id
="
echoid-s3056
"
xml:space
="
preserve
">ſit diſtantia centri oſcilla-
<
lb
/>
tionis a centro ſufpenſionis x. </
s
>
<
s
xml:id
="
echoid-s3057
"
xml:space
="
preserve
">Ponamus a, b, c, minores eſſe x, d & </
s
>
<
s
xml:id
="
echoid-s3058
"
xml:space
="
preserve
">e autern
<
lb
/>
majores.</
s
>
<
s
xml:id
="
echoid-s3059
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s3060
"
xml:space
="
preserve
">Corporum A, B, C, diſtantiæ a centro oſcillationis ſunt x-a, x-b,
<
lb
/>
x-c, & </
s
>
<
s
xml:id
="
echoid-s3061
"
xml:space
="
preserve
">corporum reliquorum diſtantiæ ab eodem centro ſunt d-x,
<
lb
/>
e-x, multiplicando corpora ſingula per ſuas diſtantias ab utroque cen-
<
lb
/>
tro, habemus Aax - Aaa + Bbx - Bbb + Ccx - Ccc = Ddd - Ddx + Eee - Eex unde
<
note
symbol
="
*
"
position
="
right
"
xlink:label
="
note-0125-06
"
xlink:href
="
note-0125-06a
"
xml:space
="
preserve
">309.</
note
>
ducimus x = {Aaa + Bbb + Ccc + Ddd + Eee/Aa + Bb + Cc + Dd + Ee}, quam eandem æquationem ha-
<
lb
/>
bemus quæcunque ex diſtantiis a, b, c, d, e, ſuperent x; </
s
>
<
s
xml:id
="
echoid-s3062
"
xml:space
="
preserve
">quare generalem hanc
<
lb
/>
detegimus regulam.</
s
>
<
s
xml:id
="
echoid-s3063
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s3064
"
xml:space
="
preserve
">Si ſingula corpora multiplicentur per quadrata ſuarum diſtantiarum à centro ſu-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0125-07
"
xlink:href
="
note-0125-07a
"
xml:space
="
preserve
">311.</
note
>
ſpenſionis, & </
s
>
<
s
xml:id
="
echoid-s3065
"
xml:space
="
preserve
">ſumma productorum dividatur per ſummam productorum ſingulorum
<
lb
/>
corporum raultiplicatorum per ſuas diſtantias ab eodem centro ſuſpenſionis, quotiens
<
lb
/>
diviſionis dabit diſtantiam inter centra ſuſpenſionis & </
s
>
<
s
xml:id
="
echoid-s3066
"
xml:space
="
preserve
">oſcillationis.</
s
>
<
s
xml:id
="
echoid-s3067
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s3068
"
xml:space
="
preserve
">Si, continuato pendulo ultra centrum ſuſpenſionis, corpora quædam
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0125-08
"
xlink:href
="
note-0125-08a
"
xml:space
="
preserve
">312.</
note
>
ſupra punctum ſuſpenſionis applicentur, horum diſtantia erit negativa; </
s
>
<
s
xml:id
="
echoid-s3069
"
xml:space
="
preserve
">Si
<
lb
/>
Ex. </
s
>
<
s
xml:id
="
echoid-s3070
"
xml:space
="
preserve
">gr. </
s
>
<
s
xml:id
="
echoid-s3071
"
xml:space
="
preserve
">talia forent corpora A&</
s
>
<
s
xml:id
="
echoid-s3072
"
xml:space
="
preserve
">B, pro + a & </
s
>
<
s
xml:id
="
echoid-s3073
"
xml:space
="
preserve
">+ b computatio ineunda foret
<
lb
/>
cum -a, -b, quorum quadrata cum etiam ſint + aa & </
s
>
<
s
xml:id
="
echoid-s3074
"
xml:space
="
preserve
">+ bb, diſtantia x in hoc ca-
<
lb
/>
ſu erit {Aaa + Bbb + Ccc + Ddd + Eee/-Aa-Bb + Cc + Dd + Ee.</
s
>
<
s
xml:id
="
echoid-s3075
"
xml:space
="
preserve
">}</
s
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s3076
"
xml:space
="
preserve
">Ut memoratam regulam applicemus lineæ cujus extremitas eſt
<
note
position
="
right
"
xlink:label
="
note-0125-09
"
xlink:href
="
note-0125-09a
"
xml:space
="
preserve
">313.</
note
>
fionis centrum, ſingula ipſius puncta, aut potius partes minimæ, multipli-
<
lb
/>
<
note
symbol
="
*
"
position
="
right
"
xlink:label
="
note-0125-10
"
xlink:href
="
note-0125-10a
"
xml:space
="
preserve
">311.</
note
>
candæ ſunt per quadrata diſtantiarum ſuarum ab extremitate, ſumma horum
<
lb
/>
<
note
symbol
="
*
"
position
="
right
"
xlink:label
="
note-0125-11
"
xlink:href
="
note-0125-11a
"
xml:space
="
preserve
">7.6. El. XII</
note
>
productorum eſt pyramis, cujus baſis eſt lineæ quadratum, & </
s
>
<
s
xml:id
="
echoid-s3077
"
xml:space
="
preserve
">altitudo ipſa
<
lb
/>
linea, ſi linea dicatur a, pyramis hæc valet {1/3}a
<
emph
style
="
super
">3</
emph
>
. </
s
>
<
s
xml:id
="
echoid-s3078
"
xml:space
="
preserve
">Dividenda hæc eſt per ſummam partium minimarum multiplicatarum per ſuas diſtantias ab extre-
<
lb
/>
<
note
symbol
="
*
"
position
="
right
"
xlink:label
="
note-0125-12
"
xlink:href
="
note-0125-12a
"
xml:space
="
preserve
">34. El. I.</
note
>
mitate, quorum productorum ſumma eſt area trianguli cujus baſis eſt a, & </
s
>
<
s
xml:id
="
echoid-s3079
"
xml:space
="
preserve
">
<
lb
/>
altitudo etiam a; </
s
>
<
s
xml:id
="
echoid-s3080
"
xml:space
="
preserve
">quæ area valet {1/2}aa . </
s
>
<
s
xml:id
="
echoid-s3081
"
xml:space
="
preserve
">Dividendo autem {1/3}a
<
emph
style
="
super
">3</
emph
>
per {1/2}a
<
emph
style
="
super
">2</
emph
>
quo- tiens eſt {2/3}a diſtantia centri oſcillationis a centro ſuſpenſionis, ut ſuperius ex-
<
lb
/>
perimento confirmavimus .</
s
>
<
s
xml:id
="
echoid-s3082
"
xml:space
="
preserve
"/>
</
p
>
<
note
symbol
="
*
"
position
="
right
"
xml:space
="
preserve
">298.</
note
>
</
div
>
</
text
>
</
echo
>