Musschenbroek, Petrus van
,
Physicae experimentales, et geometricae de magnete, tuborum capillarium vitreorumque speculorum attractione, magnitudine terrae, cohaerentia corporum firmorum dissertationes: ut et ephemerides meteorologicae ultraiectinae
Text
Text Image
Image
XML
Thumbnail overview
Document information
None
Concordance
Notes
Handwritten
Figures
Content
Thumbnails
Table of Notes
<
1 - 2
[out of range]
>
<
1 - 2
[out of range]
>
page
|<
<
(580)
of 795
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div532
"
type
="
section
"
level
="
1
"
n
="
532
">
<
p
>
<
s
xml:id
="
echoid-s14168
"
xml:space
="
preserve
">
<
pb
o
="
580
"
file
="
0596
"
n
="
597
"
rhead
="
INTRODUCTIO AD COHÆRENTIAM
"/>
chordarum in circulo, ad quadrata totidem diametrorum.</
s
>
<
s
xml:id
="
echoid-s14169
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s14170
"
xml:space
="
preserve
">Corol. </
s
>
<
s
xml:id
="
echoid-s14171
"
xml:space
="
preserve
">1. </
s
>
<
s
xml:id
="
echoid-s14172
"
xml:space
="
preserve
">Poſitis chordis circuli infinite tenuibus, omnes comple-
<
lb
/>
bunt circulum C L D L, atque omnes rectæ reſpondentes, uti A E,
<
lb
/>
G G, H H &</
s
>
<
s
xml:id
="
echoid-s14173
"
xml:space
="
preserve
">c. </
s
>
<
s
xml:id
="
echoid-s14174
"
xml:space
="
preserve
">complebunt quadratum, quare Cohærentiæ cir-
<
lb
/>
cularis baſeos aut quadratæ A E F B, forent inter ſe, uti quadratum
<
lb
/>
circuli, ad quadratum quadrati A E F B. </
s
>
<
s
xml:id
="
echoid-s14175
"
xml:space
="
preserve
">Eſt autem circulus ad qua
<
lb
/>
dratum circumſcriptum proxime, uti 157 ad 200, quornm quadrata
<
lb
/>
ſunt 24649 & </
s
>
<
s
xml:id
="
echoid-s14176
"
xml:space
="
preserve
">40000, ſecundum quam proportionem Cohærentiæ
<
lb
/>
cylindrorum parallelopipedis inſcriptorum & </
s
>
<
s
xml:id
="
echoid-s14177
"
xml:space
="
preserve
">æque longorum inve-
<
lb
/>
niendæ eſſent: </
s
>
<
s
xml:id
="
echoid-s14178
"
xml:space
="
preserve
">non tamen obſervantur in Experientiis huic propor-
<
lb
/>
tioni reſpondere Ligna; </
s
>
<
s
xml:id
="
echoid-s14179
"
xml:space
="
preserve
">an eveniat ob fibrarum flexibilitatem;
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s14180
"
xml:space
="
preserve
">velut in Propoſitione præcedenti monui; </
s
>
<
s
xml:id
="
echoid-s14181
"
xml:space
="
preserve
">an ob aliam cauſam? </
s
>
<
s
xml:id
="
echoid-s14182
"
xml:space
="
preserve
">
<
lb
/>
nondum mihi conſtat.</
s
>
<
s
xml:id
="
echoid-s14183
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s14184
"
xml:space
="
preserve
">Corol. </
s
>
<
s
xml:id
="
echoid-s14185
"
xml:space
="
preserve
">2. </
s
>
<
s
xml:id
="
echoid-s14186
"
xml:space
="
preserve
">Tab. </
s
>
<
s
xml:id
="
echoid-s14187
"
xml:space
="
preserve
">XXV. </
s
>
<
s
xml:id
="
echoid-s14188
"
xml:space
="
preserve
">fig. </
s
>
<
s
xml:id
="
echoid-s14189
"
xml:space
="
preserve
">8. </
s
>
<
s
xml:id
="
echoid-s14190
"
xml:space
="
preserve
">Si fuiſſet corpus ejusdem longitudi-
<
lb
/>
nis & </
s
>
<
s
xml:id
="
echoid-s14191
"
xml:space
="
preserve
">materiæ ac Cylindrus, cujus baſis eſſet Ellipſis Z C X D, atque
<
lb
/>
axis Ellipſeos minor C D horizontalis, X Z axis major perpendicula-
<
lb
/>
ris, productis chordis circuli oo, pp, uſque in Ellipſeos peripheriam r r,
<
lb
/>
s s. </
s
>
<
s
xml:id
="
echoid-s14192
"
xml:space
="
preserve
">atque ita porro omnibus; </
s
>
<
s
xml:id
="
echoid-s14193
"
xml:space
="
preserve
">erit Cohærentiarum ſumma in circulo, ad
<
lb
/>
eam in Ellipſi, uti quadrata chordarum oo, pp, ad quadrata ordina-
<
lb
/>
tarum in Ellipſi rr, ss: </
s
>
<
s
xml:id
="
echoid-s14194
"
xml:space
="
preserve
">ſive ut quadratum areæ circularis, ad qua-
<
lb
/>
dratum areæ Ellipticæ: </
s
>
<
s
xml:id
="
echoid-s14195
"
xml:space
="
preserve
">ſed eſt area circularis ad ellipticam, uti dia-
<
lb
/>
meter circuli C D, ad axin majorem ellipſeos X Z quare erit Co-
<
lb
/>
hærentia circuli ad eam ellipſeos, uti
<
emph
style
="
ol
">C D</
emph
>
<
emph
style
="
super
">q</
emph
>
ad
<
emph
style
="
ol
">X Z</
emph
>
<
emph
style
="
super
">q</
emph
>
.</
s
>
<
s
xml:id
="
echoid-s14196
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s14197
"
xml:space
="
preserve
">Corol. </
s
>
<
s
xml:id
="
echoid-s14198
"
xml:space
="
preserve
">3. </
s
>
<
s
xml:id
="
echoid-s14199
"
xml:space
="
preserve
">Circumſcripto circa Ellipſin C X D Z rectangulo, quod
<
lb
/>
ſit baſis parallelopipedi, erit Cohærentia baſeos Ellipticæ, ad eam
<
lb
/>
parallelopipedi, in ratione eadem ac Cohærentia baſeos circularis,
<
lb
/>
ad eam quadrati circumſcripti.</
s
>
<
s
xml:id
="
echoid-s14200
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s14201
"
xml:space
="
preserve
">Nam eſt parallelogrammum Ellipſi circumſcriptum ad aream El-
<
lb
/>
lipſeos, uti quadratum circulo circumſcriptum ad aream circuli:
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s14202
"
xml:space
="
preserve
">ſed eſt Cohærentia parallelogrammi circa Ellipſin ad Cohærentiam
<
lb
/>
Ellipſeos, uti quadrata productarum ordinatarum in ſua latera, ad
<
lb
/>
ordinatarum in Ellipſi quadrata, & </
s
>
<
s
xml:id
="
echoid-s14203
"
xml:space
="
preserve
">quia ordinatæ infinitæ implent
<
lb
/>
tandem aream Ellipſeos, uti & </
s
>
<
s
xml:id
="
echoid-s14204
"
xml:space
="
preserve
">productiones earum parallelogram-
<
lb
/>
mum, erunt Cohærentiæ uti quadrata arearum; </
s
>
<
s
xml:id
="
echoid-s14205
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s14206
"
xml:space
="
preserve
">quia areæ ſunt
<
lb
/>
proportionales areis quadrati & </
s
>
<
s
xml:id
="
echoid-s14207
"
xml:space
="
preserve
">circuli huic inſcripti, & </
s
>
<
s
xml:id
="
echoid-s14208
"
xml:space
="
preserve
">harum
<
lb
/>
Cohærentiæ uti quadrata arearum, erit Cohærentia </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>
