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
page
|<
<
(20)
of 824
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div138
"
type
="
section
"
level
="
1
"
n
="
52
">
<
p
>
<
s
xml:id
="
echoid-s1156
"
xml:space
="
preserve
">
<
pb
o
="
20
"
file
="
0050
"
n
="
50
"
rhead
="
PHYSICES ELEMENTA
"/>
ut de, fg, hi, l m, &</
s
>
<
s
xml:id
="
echoid-s1157
"
xml:space
="
preserve
">c parum admodum, ſed æqualiter, a ſe mutuo di-
<
lb
/>
ſtantibus; </
s
>
<
s
xml:id
="
echoid-s1158
"
xml:space
="
preserve
">manifeſtum eſt æquales aquæ quantitates in ſpatiis dfeg, himl,
<
lb
/>
elevari ; </
s
>
<
s
xml:id
="
echoid-s1159
"
xml:space
="
preserve
">ibique ideo dari priſmata æqualia, quorum altitudines ſunt
<
note
symbol
="
*
"
position
="
left
"
xlink:label
="
note-0050-01
"
xlink:href
="
note-0050-01a
"
xml:space
="
preserve
">77.</
note
>
ut baſes ; </
s
>
<
s
xml:id
="
echoid-s1160
"
xml:space
="
preserve
">hæ autem, quia pro parallelogrammis haberi poſſunt, & </
s
>
<
s
xml:id
="
echoid-s1161
"
xml:space
="
preserve
">propter
<
note
symbol
="
*
"
position
="
left
"
xlink:label
="
note-0050-02
"
xlink:href
="
note-0050-02a
"
xml:space
="
preserve
">34. El.
<
emph
style
="
sc
">XI</
emph
>
.</
note
>
titudines df, hl, æquales, ſunt inter ſe ut de ad hi ; </
s
>
<
s
xml:id
="
echoid-s1162
"
xml:space
="
preserve
">quæ ſunt ut d C ad h C.</
s
>
<
s
xml:id
="
echoid-s1163
"
xml:space
="
preserve
">
<
note
symbol
="
*
"
position
="
left
"
xlink:label
="
note-0050-03
"
xlink:href
="
note-0050-03a
"
xml:space
="
preserve
">1. El.
<
emph
style
="
sc
">VI</
emph
>
.</
note
>
</
s
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s1164
"
xml:space
="
preserve
">Deducimus ex his curvam efg eſſe Hyperbolam cujus Aſymptoti ſunt lineæ
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0050-04
"
xlink:href
="
note-0050-04a
"
xml:space
="
preserve
">81.</
note
>
AB, in qua vitra ſeſe mutuo tangunt, & </
s
>
<
s
xml:id
="
echoid-s1165
"
xml:space
="
preserve
">BC, ſuperficies aquæ ; </
s
>
<
s
xml:id
="
echoid-s1166
"
xml:space
="
preserve
">
<
note
position
="
left
"
xlink:label
="
note-0050-05
"
xlink:href
="
note-0050-05a
"
xml:space
="
preserve
">TAB. II.
<
lb
/>
fig. 7.</
note
>
angulum rectum ABC Hyperbola eſt æquilatera ; </
s
>
<
s
xml:id
="
echoid-s1167
"
xml:space
="
preserve
">examinavimus
<
note
symbol
="
*
"
position
="
left
"
xlink:label
="
note-0050-06
"
xlink:href
="
note-0050-06a
"
xml:space
="
preserve
">La Hire
<
lb
/>
<
emph
style
="
sc
">S. C</
emph
>
. l.
<
emph
style
="
sc
">IV</
emph
>
.
<
lb
/>
p. 2.</
note
>
caſum in quo linea, in qua vitra ſeſe mutuo tangunt, ad ſuperficiem aquæ
<
lb
/>
perpendicularis eſt.</
s
>
<
s
xml:id
="
echoid-s1168
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s1169
"
xml:space
="
preserve
">Facile etiam confertur altitudo in tubo cum altitudine inter plana.</
s
>
<
s
xml:id
="
echoid-s1170
"
xml:space
="
preserve
"/>
</
p
>
<
note
symbol
="
*
"
position
="
left
"
xml:space
="
preserve
">ibid. l.
<
emph
style
="
sc
">V</
emph
>
.
<
lb
/>
p. 13.</
note
>
<
p
>
<
s
xml:id
="
echoid-s1171
"
xml:space
="
preserve
">Sit tubi cylindrici ſectio M, cujus ſemidiameter æqualis eſt diſtantiæ e d inter
<
lb
/>
plana. </
s
>
<
s
xml:id
="
echoid-s1172
"
xml:space
="
preserve
">Clarum eſt vim, quæ ſuſtinet priſma aqueum cujus baſis eſt def pro-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0050-08
"
xlink:href
="
note-0050-08a
"
xml:space
="
preserve
">82.</
note
>
portionem ſequi lineæ df; </
s
>
<
s
xml:id
="
echoid-s1173
"
xml:space
="
preserve
">ambabus enim df & </
s
>
<
s
xml:id
="
echoid-s1174
"
xml:space
="
preserve
">eg proportionalis eſt vis quæ pa-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0050-09
"
xlink:href
="
note-0050-09a
"
xml:space
="
preserve
">TAB I.
<
lb
/>
fig. 7.</
note
>
rallelopipedum, cujus baſis eſt dfeg, ſuſtinet .</
s
>
<
s
xml:id
="
echoid-s1175
"
xml:space
="
preserve
">
<
note
symbol
="
*
"
position
="
left
"
xlink:label
="
note-0050-10
"
xlink:href
="
note-0050-10a
"
xml:space
="
preserve
">77.</
note
>
</
s
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s1176
"
xml:space
="
preserve
">In tubo vis quæ ſuſtinet priſma, cujus baſis eſt nop, proportionalis eſt ipſi np;
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s1177
"
xml:space
="
preserve
">quia tota circumferentia proportionalis eſt illi quæ integrum aqueum cylin-
<
lb
/>
drum vitro contentum ſuſtinet. </
s
>
<
s
xml:id
="
echoid-s1178
"
xml:space
="
preserve
">Si np & </
s
>
<
s
xml:id
="
echoid-s1179
"
xml:space
="
preserve
">df fuerint æquales; </
s
>
<
s
xml:id
="
echoid-s1180
"
xml:space
="
preserve
">vires quæ pri-
<
lb
/>
ſmata ſuſtinent æquales ſunt; </
s
>
<
s
xml:id
="
echoid-s1181
"
xml:space
="
preserve
">ideoque & </
s
>
<
s
xml:id
="
echoid-s1182
"
xml:space
="
preserve
">ipſa priſmata æqualia; </
s
>
<
s
xml:id
="
echoid-s1183
"
xml:space
="
preserve
">ſunt etiam
<
lb
/>
in hoc caſu baſes nop, def, æquales, quare priſmatum altitudines non
<
lb
/>
difterunt, & </
s
>
<
s
xml:id
="
echoid-s1184
"
xml:space
="
preserve
">aqua in tubum & </
s
>
<
s
xml:id
="
echoid-s1185
"
xml:space
="
preserve
">inter plana ad eandem adſcendit altitudinem.</
s
>
<
s
xml:id
="
echoid-s1186
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s1187
"
xml:space
="
preserve
">Variarimultis modis poteſt experimentum de adſcenſu aquæ inter plana.</
s
>
<
s
xml:id
="
echoid-s1188
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s1189
"
xml:space
="
preserve
">Nimium longum & </
s
>
<
s
xml:id
="
echoid-s1190
"
xml:space
="
preserve
">ſatis inutile foret, omnia quæ huc ſpectant perpendere;
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s1191
"
xml:space
="
preserve
">ſatis eſt caſum præcipuum examinaſſe; </
s
>
<
s
xml:id
="
echoid-s1192
"
xml:space
="
preserve
">Circa duos alios in quibus angulus
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0050-11
"
xlink:href
="
note-0050-11a
"
xml:space
="
preserve
">83.</
note
>
ABC, quem linea, in qua vitra junguntur, cum ſuperficie aquæ efficit, eſt
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0050-12
"
xlink:href
="
note-0050-12a
"
xml:space
="
preserve
">TAB. I.
<
lb
/>
fig. 8. 9.</
note
>
acutus aut obtuſus, manentibus planis vitreis ad aquæ ſuperficiem perpendi-
<
lb
/>
cularibus, notabo, aquam etiam terminari Hyperbolica linea, cujus aſym-
<
lb
/>
ptos una eſt aquæ ſuperficies, altera habetur erigendo perpendicularem BF
<
lb
/>
ad CB, in puncto B, aſvmptos quæſita erit BE, quæ dividit bifariam FD,
<
lb
/>
perpendicularem in puncto quocunque ad BF, & </
s
>
<
s
xml:id
="
echoid-s1193
"
xml:space
="
preserve
">terminatam linea BA.</
s
>
<
s
xml:id
="
echoid-s1194
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s1195
"
xml:space
="
preserve
">Si DF per punctum D Hyperbolæ tranſect, BF erit ſemidiameter con-
<
lb
/>
jugata cum ſemidiametro BD.</
s
>
<
s
xml:id
="
echoid-s1196
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s1197
"
xml:space
="
preserve
">In Fig. </
s
>
<
s
xml:id
="
echoid-s1198
"
xml:space
="
preserve
">9. </
s
>
<
s
xml:id
="
echoid-s1199
"
xml:space
="
preserve
">ultra F Hyperbola non continuatur; </
s
>
<
s
xml:id
="
echoid-s1200
"
xml:space
="
preserve
">aqua tamen ulterius adſcen-
<
lb
/>
dit, ſed aliâ terminatur Curvâ.</
s
>
<
s
xml:id
="
echoid-s1201
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s1202
"
xml:space
="
preserve
">In Fig. </
s
>
<
s
xml:id
="
echoid-s1203
"
xml:space
="
preserve
">8. </
s
>
<
s
xml:id
="
echoid-s1204
"
xml:space
="
preserve
">licet Hyperbola vitrorum latera juncta ſecet in D non ibi ad-
<
lb
/>
ſcenſus aquæ terminatur, ſed ad certam, & </
s
>
<
s
xml:id
="
echoid-s1205
"
xml:space
="
preserve
">quidem pro diverſo, quem in-
<
lb
/>
ter ſe vitra continent, angulo, diverſam ab AB diſtantiam, ab Hyperbola
<
lb
/>
deflectitur curva, adſcenſuſque juxta BA continuatur. </
s
>
<
s
xml:id
="
echoid-s1206
"
xml:space
="
preserve
">Ubi enim exigua
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0050-13
"
xlink:href
="
note-0050-13a
"
xml:space
="
preserve
">84.</
note
>
admodum eſt inter vitra diſtantia attractiones oppoſitæ ſeſe mutuo juvant, quo au-
<
lb
/>
getur aquæ adſcenſus. </
s
>
<
s
xml:id
="
echoid-s1207
"
xml:space
="
preserve
">Simile augmentum actionis in n ſequenti memoratur;
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s1208
"
xml:space
="
preserve
">in luminis attractione a corporibus etiam locum habet, ut notamus in nume-
<
lb
/>
ro ultimo cap. </
s
>
<
s
xml:id
="
echoid-s1209
"
xml:space
="
preserve
">5. </
s
>
<
s
xml:id
="
echoid-s1210
"
xml:space
="
preserve
">lib. </
s
>
<
s
xml:id
="
echoid-s1211
"
xml:space
="
preserve
">3.</
s
>
<
s
xml:id
="
echoid-s1212
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div144
"
type
="
section
"
level
="
1
"
n
="
53
">
<
head
xml:id
="
echoid-head93
"
style
="
it
"
xml:space
="
preserve
">De motu guttæ in n. 59,</
head
>
<
p
>
<
s
xml:id
="
echoid-s1213
"
xml:space
="
preserve
">Concipiamus plana, inter quæ gutta movetur, ſecari plano ad plana, & </
s
>
<
s
xml:id
="
echoid-s1214
"
xml:space
="
preserve
">ad
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0050-14
"
xlink:href
="
note-0050-14a
"
xml:space
="
preserve
">85.</
note
>
lineam in qua junguntur perpendicularem: </
s
>
<
s
xml:id
="
echoid-s1215
"
xml:space
="
preserve
">repræſentatur ſectio hæc; </
s
>
<
s
xml:id
="
echoid-s1216
"
xml:space
="
preserve
">ſed, cum
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0050-15
"
xlink:href
="
note-0050-15a
"
xml:space
="
preserve
">TAB. I.
<
lb
/>
fig. 10.</
note
>
motus ab inclinatione planorum ad ſe invicem pendeat, hanc juſto majorem
<
lb
/>
repræſentamus, ut & </
s
>
<
s
xml:id
="
echoid-s1217
"
xml:space
="
preserve
">diſtantiam inter vitra, & </
s
>
<
s
xml:id
="
echoid-s1218
"
xml:space
="
preserve
">diſtantiam ad quam vitrum in
<
lb
/>
oleum agit.</
s
>
<
s
xml:id
="
echoid-s1219
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s1220
"
xml:space
="
preserve
">Sint plana AB, CD; </
s
>
<
s
xml:id
="
echoid-s1221
"
xml:space
="
preserve
">gutta e eff; </
s
>
<
s
xml:id
="
echoid-s1222
"
xml:space
="
preserve
">gh diſtantia ad quam vitrum oleum tra-
<
lb
/>
hit: </
s
>
<
s
xml:id
="
echoid-s1223
"
xml:space
="
preserve
">omne ergo oleum inter iehf ad planum trahitur, & </
s
>
<
s
xml:id
="
echoid-s1224
"
xml:space
="
preserve
">conatur ſeſe </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>