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
|<
<
(107)
of 824
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div654
"
type
="
section
"
level
="
1
"
n
="
185
">
<
p
>
<
s
xml:id
="
echoid-s4502
"
xml:space
="
preserve
">
<
pb
o
="
107
"
file
="
0165
"
n
="
179
"
rhead
="
MATHEMATICA. LIB. I. CAP. XXI.
"/>
eo ſi hæc dicatur 2R, erit IL = {AI
<
emph
style
="
super
">q</
emph
>
/2R} = {Bi
<
emph
style
="
super
">q</
emph
>
/2R}:</
s
>
<
s
xml:id
="
echoid-s4503
"
xml:space
="
preserve
">ſed{aB
<
emph
style
="
super
">q</
emph
>
/2AF} ſe habet ad {Bi
<
emph
style
="
super
">q</
emph
>
/2R},
<
lb
/>
ut {
<
emph
style
="
ol
">M-N</
emph
>
<
emph
style
="
super
">q</
emph
>
/AF} ad{N
<
emph
style
="
super
">q</
emph
>
/R}; </
s
>
<
s
xml:id
="
echoid-s4504
"
xml:space
="
preserve
">idcirco
<
lb
/>
IL, AB:</
s
>
<
s
xml:id
="
echoid-s4505
"
xml:space
="
preserve
">: {N
<
emph
style
="
super
">q</
emph
>
/R} {
<
emph
style
="
ol
">M-N</
emph
>
<
emph
style
="
super
">q</
emph
>
/AF}</
s
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s4506
"
xml:space
="
preserve
">Sed ut vidimus AB, I i:</
s
>
<
s
xml:id
="
echoid-s4507
"
xml:space
="
preserve
">: M-N, M + N; </
s
>
<
s
xml:id
="
echoid-s4508
"
xml:space
="
preserve
">ergo ex compoſitione rationis
<
lb
/>
IL, I i:</
s
>
<
s
xml:id
="
echoid-s4509
"
xml:space
="
preserve
">: {N
<
emph
style
="
super
">q</
emph
>
x
<
emph
style
="
ol
">M-N</
emph
>
/R}, {
<
emph
style
="
ol
">M-N</
emph
>
<
emph
style
="
super
">q</
emph
>
x
<
emph
style
="
ol
">M + N</
emph
>
/AF} = {
<
emph
style
="
ol
">M
<
emph
style
="
super
">q</
emph
>
-N
<
emph
style
="
super
">q</
emph
>
</
emph
>
x
<
emph
style
="
ol
">M-N</
emph
>
/AF} :</
s
>
<
s
xml:id
="
echoid-s4510
"
xml:space
="
preserve
">: {N
<
emph
style
="
super
">q</
emph
>
/R}, {M
<
emph
style
="
super
">q</
emph
>
-N
<
emph
style
="
super
">q</
emph
>
/AF}
<
lb
/>
Eodem tempore percurruntur IL & </
s
>
<
s
xml:id
="
echoid-s4511
"
xml:space
="
preserve
">i I, prima vi qua corpus retinetur in
<
lb
/>
Ellipſi quieſcente, ſecunda difterentiâ vis hujus cum vi qua corpus in El-
<
lb
/>
lipſi mobili retinetur, ergo vis in Ellipſi ad differentiam hanc, ut {N
<
emph
style
="
super
">q</
emph
>
/R}
<
lb
/>
ad {M
<
emph
style
="
super
">q</
emph
>
-N
<
emph
style
="
super
">q</
emph
>
/AF} .</
s
>
<
s
xml:id
="
echoid-s4512
"
xml:space
="
preserve
"/>
</
p
>
<
note
symbol
="
*
"
position
="
right
"
xml:space
="
preserve
">401.</
note
>
<
p
>
<
s
xml:id
="
echoid-s4513
"
xml:space
="
preserve
">Dicatur {N
<
emph
style
="
super
">q</
emph
>
/AF
<
emph
style
="
super
">q</
emph
>
} vis qua corpus in Ellipſi retinetur in puncto A, & </
s
>
<
s
xml:id
="
echoid-s4514
"
xml:space
="
preserve
">fiat
<
lb
/>
{N
<
emph
style
="
super
">q</
emph
>
/R}, {M
<
emph
style
="
super
">q</
emph
>
-N
<
emph
style
="
super
">q</
emph
>
/AF} :</
s
>
<
s
xml:id
="
echoid-s4515
"
xml:space
="
preserve
">: {N
<
emph
style
="
super
">q</
emph
>
/AF
<
emph
style
="
super
">q</
emph
>
}, ad differentiam virium {RMM-RNN/AF
<
emph
style
="
super
">c</
emph
>
}</
s
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s4516
"
xml:space
="
preserve
">Si agatur de diſtantia alia quæcunque quæ dicatur D, vis qua corpus reti-
<
lb
/>
netur in Ellipſi hac analogia detegitur
<
note
symbol
="
*
"
position
="
right
"
xlink:label
="
note-0165-02
"
xlink:href
="
note-0165-02a
"
xml:space
="
preserve
">381. 411.</
note
>
{I/AF
<
emph
style
="
super
">q</
emph
>
}, {I/D
<
emph
style
="
super
">q</
emph
>
} :</
s
>
<
s
xml:id
="
echoid-s4517
"
xml:space
="
preserve
">: {N
<
emph
style
="
super
">q</
emph
>
/AF
<
emph
style
="
super
">q</
emph
>
} ad vim quæſitam {NN/DD}.</
s
>
<
s
xml:id
="
echoid-s4518
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s4519
"
xml:space
="
preserve
">Difterentia virium detegitur hac regulâ
<
note
symbol
="
*
"
position
="
right
"
xlink:label
="
note-0165-03
"
xlink:href
="
note-0165-03a
"
xml:space
="
preserve
">410.</
note
>
{I/AF
<
emph
style
="
super
">c</
emph
>
}, {I/D
<
emph
style
="
super
">c</
emph
>
} :</
s
>
<
s
xml:id
="
echoid-s4520
"
xml:space
="
preserve
">: {RMM-RNN/AF
<
emph
style
="
super
">c</
emph
>
} ad differentiam quæſitam
<
lb
/>
{RMM-RNN/D
<
emph
style
="
super
">c</
emph
>
}.</
s
>
<
s
xml:id
="
echoid-s4521
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s4522
"
xml:space
="
preserve
">Idcirco vis integra qua corpus in Ellipſi mobili retinetur ſequitur propor-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0165-04
"
xlink:href
="
note-0165-04a
"
xml:space
="
preserve
">427.</
note
>
tionem {NN/D
<
emph
style
="
super
">q</
emph
>
} + {RMM-RNN/D
<
emph
style
="
super
">c</
emph
>
}, quando corpus & </
s
>
<
s
xml:id
="
echoid-s4523
"
xml:space
="
preserve
">Ellipſis ad eandem
<
lb
/>
partem tendunt. </
s
>
<
s
xml:id
="
echoid-s4524
"
xml:space
="
preserve
">Si motus hi fuerint contrarii vis proportionalis eſt
<
lb
/>
{NN/D
<
emph
style
="
super
">q</
emph
>
}-{RMM - RNN/D
<
emph
style
="
super
">c</
emph
>
}.</
s
>
<
s
xml:id
="
echoid-s4525
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
</
text
>
</
echo
>
