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 handwritten notes
<
1 - 5
[out of range]
>
<
1 - 5
[out of range]
>
page
|<
<
(113)
of 824
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div671
"
type
="
section
"
level
="
1
"
n
="
187
">
<
p
>
<
s
xml:id
="
echoid-s4657
"
xml:space
="
preserve
">
<
pb
o
="
113
"
file
="
0173
"
n
="
188
"
rhead
="
MATHEMATICA. LIB. I. CAR. XXII.
"/>
vim corpori communicant; </
s
>
<
s
xml:id
="
echoid-s4658
"
xml:space
="
preserve
">cûm autem elaſteria ſint æqua-
<
lb
/>
lia, vires ſunt ut numeri Elaſteriorum, quorum expanſione
<
lb
/>
communicantur. </
s
>
<
s
xml:id
="
echoid-s4659
"
xml:space
="
preserve
">Corpus verò expanſione Elaſteriorum non
<
lb
/>
poteſt celeritatem acquirere, miſi motu accelerato, ita ut
<
lb
/>
per ſingulos gradus minores velocitatis tranſeat. </
s
>
<
s
xml:id
="
echoid-s4660
"
xml:space
="
preserve
">Sit A F
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0173-01
"
xlink:href
="
note-0173-01a
"
xml:space
="
preserve
">
<
emph
style
="
sc
">TAB. XVL.</
emph
>
<
lb
/>
fig. 2.</
note
>
celeritas corporis; </
s
>
<
s
xml:id
="
echoid-s4661
"
xml:space
="
preserve
">A b, bc, cd, & </
s
>
<
s
xml:id
="
echoid-s4662
"
xml:space
="
preserve
">c. </
s
>
<
s
xml:id
="
echoid-s4663
"
xml:space
="
preserve
">gradus infinitè exi-
<
lb
/>
gui celeritatis, A b primus, bc ſecundus, & </
s
>
<
s
xml:id
="
echoid-s4664
"
xml:space
="
preserve
">c. </
s
>
<
s
xml:id
="
echoid-s4665
"
xml:space
="
preserve
">per quos o-
<
lb
/>
mnes tranſit corpus antequam acquirat celeritatem AF.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s4666
"
xml:space
="
preserve
">Parallelogramma A bhe, bcif, cdlg, & </
s
>
<
s
xml:id
="
echoid-s4667
"
xml:space
="
preserve
">c ſunt in-
<
lb
/>
ter ſe reſpectivè, ut numeri Elaſteriorum, quibus gradus
<
lb
/>
velocitatis primus, ſecundus, tertius, &</
s
>
<
s
xml:id
="
echoid-s4668
"
xml:space
="
preserve
">c. </
s
>
<
s
xml:id
="
echoid-s4669
"
xml:space
="
preserve
">acquiruntur; </
s
>
<
s
xml:id
="
echoid-s4670
"
xml:space
="
preserve
">
<
lb
/>
ideoque areæ A dle, AFG e, ſunt inter ſe ut numerie-
<
lb
/>
laſteriorum, quibus velocitates A d, AF acquiruntur, id
<
lb
/>
eſt ſunt hæ areæ inter ſe ut Vires ejuſdem corporis, aut
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0173-02
"
xlink:href
="
note-0173-02a
"
xml:space
="
preserve
">447.</
note
>
duorum corporum æqualium, hiſce velocitatibus motorum;
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s4671
"
xml:space
="
preserve
">eùm autem lineæ A e, eh, bf, fi, & </
s
>
<
s
xml:id
="
echoid-s4672
"
xml:space
="
preserve
">c. </
s
>
<
s
xml:id
="
echoid-s4673
"
xml:space
="
preserve
">ſint infinitè exi-
<
lb
/>
guæ; </
s
>
<
s
xml:id
="
echoid-s4674
"
xml:space
="
preserve
">areæ A dle, AFG e à triangulis ſimilibus adl, afg,
<
lb
/>
non differunt, & </
s
>
<
s
xml:id
="
echoid-s4675
"
xml:space
="
preserve
">ſunt inter ſe ut quadrata laterum homolo-
<
lb
/>
gorum , aut velocitatum A d, AF, quod
<
note
symbol
="
*
"
position
="
right
"
xlink:label
="
note-0173-03
"
xlink:href
="
note-0173-03a
"
xml:space
="
preserve
">19. El.
<
lb
/>
<
emph
style
="
sc
">VI</
emph
>
.</
note
>
experimentis; </
s
>
<
s
xml:id
="
echoid-s4676
"
xml:space
="
preserve
">ſed pauca antea præmittenda ſunt.</
s
>
<
s
xml:id
="
echoid-s4677
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s4678
"
xml:space
="
preserve
">Vires eſſe inter ſe ut quadrata velocitatum, aliis demon-
<
lb
/>
ſtrationibus, quæ ex principiis quæ nil inter ſe, neque cum
<
lb
/>
his quæ hìc ponuntur commune habent, deductis, in ſequenti-
<
lb
/>
bus etiam demonſtrabo, ubi de viribus obliquis, & </
s
>
<
s
xml:id
="
echoid-s4679
"
xml:space
="
preserve
">de reſiſten-
<
lb
/>
tia fluidorum, agam.</
s
>
<
s
xml:id
="
echoid-s4680
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s4681
"
xml:space
="
preserve
">Vires, quas corpus cadendo acquirit, ſunt ut altitudines,
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0173-04
"
xlink:href
="
note-0173-04a
"
xml:space
="
preserve
">448.</
note
>
quas cadendo percurrit, ab initio caſits; </
s
>
<
s
xml:id
="
echoid-s4682
"
xml:space
="
preserve
">ſunt enim hæ ut
<
lb
/>
quadrata velocitatum in fine deſcenſus . </
s
>
<
s
xml:id
="
echoid-s4683
"
xml:space
="
preserve
">Cum
<
note
symbol
="
*
"
position
="
right
"
xlink:label
="
note-0173-05
"
xlink:href
="
note-0173-05a
"
xml:space
="
preserve
">255.</
note
>
hæc ſequentibus Experimentis immediatè demonſtretur,
<
lb
/>
patet gravitatem, quæ æqualibus temporibus æquales corpo-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0173-06
"
xlink:href
="
note-0173-06a
"
xml:space
="
preserve
">419.</
note
>
ri communicat gradus celeritatis, non iidem æquales
<
note
symbol
="
*
"
position
="
right
"
xlink:label
="
note-0173-07
"
xlink:href
="
note-0173-07a
"
xml:space
="
preserve
">251.</
note
>
vis communicare, ſed illud, quo corpus ad Tellurem
<
note
symbol
="
*
"
position
="
right
"
xlink:label
="
note-0173-08
"
xlink:href
="
note-0173-08a
"
xml:space
="
preserve
">442.</
note
>
dit, cum ipſo corpore moveri , dum in corpus
<
note
symbol
="
*
"
position
="
right
"
xlink:label
="
note-0173-09
"
xlink:href
="
note-0173-09a
"
xml:space
="
preserve
">439.</
note
>
agit, ut in quieſcens.</
s
>
<
s
xml:id
="
echoid-s4684
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s4685
"
xml:space
="
preserve
">Si corpora fuerint inæqualia, æqualibus velocitatibus
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0173-10
"
xlink:href
="
note-0173-10a
"
xml:space
="
preserve
">450.</
note
>
mota, vires inſitæ ſunt inter ſe ut quantitates materiæ </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>