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
Table of figures
<
1 - 30
31 - 60
61 - 90
91 - 98
[out of range]
>
<
1 - 30
31 - 60
61 - 90
91 - 98
[out of range]
>
page
|<
<
(68)
of 824
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div446
"
type
="
section
"
level
="
1
"
n
="
150
">
<
p
>
<
s
xml:id
="
echoid-s2854
"
xml:space
="
preserve
">
<
pb
o
="
68
"
file
="
0118
"
n
="
128
"
rhead
="
PHYSICES ELEMENTA
"/>
mus, ita ut filum longitudinis BC æquale ſit curvæ
<
lb
/>
CA; </
s
>
<
s
xml:id
="
echoid-s2855
"
xml:space
="
preserve
">quare tota curva ABD dupla eſt lineæ CB; </
s
>
<
s
xml:id
="
echoid-s2856
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s2857
"
xml:space
="
preserve
">
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0118-01
"
xlink:href
="
note-0118-01a
"
xml:space
="
preserve
">284.</
note
>
quadrupla axis FB.</
s
>
<
s
xml:id
="
echoid-s2858
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s2859
"
xml:space
="
preserve
">In eodem ſcholio demonſtramus. </
s
>
<
s
xml:id
="
echoid-s2860
"
xml:space
="
preserve
">Tangentem ad curvam
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0118-02
"
xlink:href
="
note-0118-02a
"
xml:space
="
preserve
">285.</
note
>
in puncto, ut P, parallelam eſſe chordæ EB, in circulo
<
lb
/>
FBE ductæ ad punctum infimum B ex puncto E, in quo cir-
<
lb
/>
culus ſecatur à lineâ PE parrallela ad baſim AD & </
s
>
<
s
xml:id
="
echoid-s2861
"
xml:space
="
preserve
">per
<
lb
/>
P tranſeunti: </
s
>
<
s
xml:id
="
echoid-s2862
"
xml:space
="
preserve
">Ut & </
s
>
<
s
xml:id
="
echoid-s2863
"
xml:space
="
preserve
">portionem PB curvæ æqualem eſſe
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0118-03
"
xlink:href
="
note-0118-03a
"
xml:space
="
preserve
">286.</
note
>
duplæ chordæ EB.</
s
>
<
s
xml:id
="
echoid-s2864
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s2865
"
xml:space
="
preserve
">Cum autem in ſingulis curvæ punctis corpus in curva de-
<
lb
/>
ſcendat juxta directionem tangentis ad curvam, ſequi-
<
lb
/>
tur corpus in puncto quocunque curvæ conari deſcendere
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0118-04
"
xlink:href
="
note-0118-04a
"
xml:space
="
preserve
">287.</
note
>
cumvi, quæ proportionalis portioni curvæ inter hoccepun-
<
lb
/>
ctum & </
s
>
<
s
xml:id
="
echoid-s2866
"
xml:space
="
preserve
">curvæ punctum infimum B . </
s
>
<
s
xml:id
="
echoid-s2867
"
xml:space
="
preserve
">Unde patet, ſi
<
note
symbol
="
*
"
position
="
left
"
xlink:label
="
note-0118-05
"
xlink:href
="
note-0118-05a
"
xml:space
="
preserve
">267 285.
<
lb
/>
286.</
note
>
pendula ut CP ab altitudinibus diverſis, eodem momento,
<
lb
/>
dimittantur, celeritates, quibus cadere incipiunt, eſſe in-
<
lb
/>
ter ſe, ut ſpatia percurrenda, antequam ad B perveniant:
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s2868
"
xml:space
="
preserve
">ſi ergo iſtis celeritatibus ſolis, motu non accelerato, agita-
<
lb
/>
rentur, eodem temporis momento ad B pervenirent ; </
s
>
<
s
xml:id
="
echoid-s2869
"
xml:space
="
preserve
">
<
note
symbol
="
*
"
position
="
left
"
xlink:label
="
note-0118-06
"
xlink:href
="
note-0118-06a
"
xml:space
="
preserve
">94.</
note
>
dem modo velocitatibus ſecundo momento acquiſitis, et-
<
lb
/>
iam ad B eodem momento pertingunt; </
s
>
<
s
xml:id
="
echoid-s2870
"
xml:space
="
preserve
">idemque ratioci-
<
lb
/>
nium pro momentis ſequentibus procedit; </
s
>
<
s
xml:id
="
echoid-s2871
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s2872
"
xml:space
="
preserve
">ſemi vibra-
<
lb
/>
tiones ex omnibus celeritatibus junctis utcunque inæquales,
<
lb
/>
ut & </
s
>
<
s
xml:id
="
echoid-s2873
"
xml:space
="
preserve
">vibrationes integræ, iiſdem temporibus peraguntur.</
s
>
<
s
xml:id
="
echoid-s2874
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s2875
"
xml:space
="
preserve
">Ulterius in primo ſcholio demonſtramus. </
s
>
<
s
xml:id
="
echoid-s2876
"
xml:space
="
preserve
">Tempus unius
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0118-07
"
xlink:href
="
note-0118-07a
"
xml:space
="
preserve
">288.</
note
>
cujuſque vibrationis eſſe ad tempus caſus verticalis, per ſe-
<
lb
/>
milongitudinem penduli, ut peripheria circuli, ad diame-
<
lb
/>
trum. </
s
>
<
s
xml:id
="
echoid-s2877
"
xml:space
="
preserve
">In hac curva pars infima cum circuli arcu exiguo ad
<
lb
/>
ſenſum coincidit; </
s
>
<
s
xml:id
="
echoid-s2878
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s2879
"
xml:space
="
preserve
">hæc eſt vera ratio, quare in circulo
<
lb
/>
tempora vibrationum exiguarum, utcunque inæqualium,
<
lb
/>
ſint æqualia; </
s
>
<
s
xml:id
="
echoid-s2880
"
xml:space
="
preserve
">ideo etiam duratio harum vibrationum ad du-
<
lb
/>
rationem vibrationis per chordas, id eſt ad tempus caſus
<
lb
/>
verticalis per longitudinem octuplam longitudinis penduli
<
note
symbol
="
*
"
position
="
left
"
xlink:label
="
note-0118-08
"
xlink:href
="
note-0118-08a
"
xml:space
="
preserve
">279.</
note
>
aut ſedecuplam ſemi longitudinis penduli, illam habet ra-
<
lb
/>
tionem, quæ datur inter peripheriam circuli & </
s
>
<
s
xml:id
="
echoid-s2881
"
xml:space
="
preserve
">quatuor diame-
<
lb
/>
tros , id eſt circiter ut 785 ad 1000: </
s
>
<
s
xml:id
="
echoid-s2882
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s2883
"
xml:space
="
preserve
">celerius per
<
note
symbol
="
*
"
position
="
left
"
xlink:label
="
note-0118-09
"
xlink:href
="
note-0118-09a
"
xml:space
="
preserve
">255.
<
lb
/>
289.</
note
>
</
s
>
</
p
>
</
div
>
</
text
>
</
echo
>
