Stevin, Simon
,
Mathematicorum hypomnematum... : T. 4: De Statica : cum appendice et additamentis
,
1605
Text
Text Image
Image
XML
Thumbnail overview
Document information
None
Concordance
Notes
Figures
Content
Thumbnails
page
|<
<
(44)
of 197
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div207
"
type
="
section
"
level
="
1
"
n
="
150
">
<
pb
o
="
44
"
file
="
527.01.044
"
n
="
44
"
rhead
="
1 L*IBER* S*TATIC Æ*
"/>
</
div
>
<
div
xml:id
="
echoid-div208
"
type
="
section
"
level
="
1
"
n
="
151
">
<
head
xml:id
="
echoid-head163
"
xml:space
="
preserve
">DEMONSTRATIO.</
head
>
<
p
>
<
s
xml:id
="
echoid-s1335
"
xml:space
="
preserve
">Quemadmodũ AS ad S OE: </
s
>
<
s
xml:id
="
echoid-s1336
"
xml:space
="
preserve
">ita rectè extol-
<
lb
/>
<
figure
xlink:label
="
fig-527.01.044-01
"
xlink:href
="
fig-527.01.044-01a
"
number
="
75
">
<
image
file
="
527.01.044-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.044-01
"/>
</
figure
>
lens põdus ad Y extollĕs obliquè, per 20 propoſ.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s1337
"
xml:space
="
preserve
">Atqui triangulũ Æ OE Z triangulo OE S A ſimi-
<
lb
/>
le eſt, quorum homologa latera ſunt, OE Z cum
<
lb
/>
OE S, & </
s
>
<
s
xml:id
="
echoid-s1338
"
xml:space
="
preserve
">Z Æ, cum S A. </
s
>
<
s
xml:id
="
echoid-s1339
"
xml:space
="
preserve
">erit igitur quemadmo-
<
lb
/>
dum A S ad S OE: </
s
>
<
s
xml:id
="
echoid-s1340
"
xml:space
="
preserve
">ita Æ Z ad Z OE, & </
s
>
<
s
xml:id
="
echoid-s1341
"
xml:space
="
preserve
">con-
<
lb
/>
ſequenter quemadmodum Æ Z 2 ad Z OE 1: </
s
>
<
s
xml:id
="
echoid-s1342
"
xml:space
="
preserve
">ita
<
lb
/>
pondus rectè extollens 4 lib. </
s
>
<
s
xml:id
="
echoid-s1343
"
xml:space
="
preserve
">ad Y. </
s
>
<
s
xml:id
="
echoid-s1344
"
xml:space
="
preserve
">Innotuit igi-
<
lb
/>
tur Y 2 ℔ pendere, quod probandum ſuit. </
s
>
<
s
xml:id
="
echoid-s1345
"
xml:space
="
preserve
">Si-
<
lb
/>
militer in quibuſvis aliis exemplis proceditur.</
s
>
<
s
xml:id
="
echoid-s1346
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s1347
"
xml:space
="
preserve
">C*ONCLVSIO*. </
s
>
<
s
xml:id
="
echoid-s1348
"
xml:space
="
preserve
">Datis igitur, notâ columnâ
<
lb
/>
punctis q́ue in axe ſirmo, &</
s
>
<
s
xml:id
="
echoid-s1349
"
xml:space
="
preserve
">c.</
s
>
<
s
xml:id
="
echoid-s1350
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div210
"
type
="
section
"
level
="
1
"
n
="
152
">
<
head
xml:id
="
echoid-head164
"
xml:space
="
preserve
">1 NOTA.</
head
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s1351
"
xml:space
="
preserve
">Etiamiſto pacto concludere licuiſſet: </
s
>
<
s
xml:id
="
echoid-s1352
"
xml:space
="
preserve
">AS 2 dat S OE 1: </
s
>
<
s
xml:id
="
echoid-s1353
"
xml:space
="
preserve
">ego pondus 4 ℔ rectè
<
unsure
/>
ex-
<
lb
/>
t
<
unsure
/>
ollens dabit γ 2 ℔. </
s
>
<
s
xml:id
="
echoid-s1354
"
xml:space
="
preserve
">Verum ut operatio ipſirei & </
s
>
<
s
xml:id
="
echoid-s1355
"
xml:space
="
preserve
">natur æ magis conformis ſit (intra
<
lb
/>
ſolidx
<
unsure
/>
m corpus enim AS & </
s
>
<
s
xml:id
="
echoid-s1356
"
xml:space
="
preserve
">S OE delineari nequeunt ) externam perpendicularen
<
unsure
/>
s
<
lb
/>
in exemplo pro internâ aſſumere placuit.</
s
>
<
s
xml:id
="
echoid-s1357
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div211
"
type
="
section
"
level
="
1
"
n
="
153
">
<
head
xml:id
="
echoid-head165
"
xml:space
="
preserve
">2 NOTA.</
head
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s1358
"
xml:space
="
preserve
">Quomodo autem terminus ignotus, ut pondus rectè extollens, linea tam rectè. </
s
>
<
s
xml:id
="
echoid-s1359
"
xml:space
="
preserve
">quàns
<
lb
/>
obliquè extollens, columna, datis tribus inversâ & </
s
>
<
s
xml:id
="
echoid-s1360
"
xml:space
="
preserve
">alternâ proportione innoteſcat, igno-
<
lb
/>
tum eſſe non poteſt, quapropter brevitati ſtudentes, omittemus.</
s
>
<
s
xml:id
="
echoid-s1361
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div212
"
type
="
section
"
level
="
1
"
n
="
154
">
<
head
xml:id
="
echoid-head166
"
xml:space
="
preserve
">14 THE OREMA. 23 PROPOSITIO.</
head
>
<
p
>
<
s
xml:id
="
echoid-s1362
"
xml:space
="
preserve
">Æqualia pondera ſuſpenſa de ductariis lineis, quæ ex
<
lb
/>
eodem axis puncto in contrarias partes ductę æquales cum
<
lb
/>
axe angulos faciunt: </
s
>
<
s
xml:id
="
echoid-s1363
"
xml:space
="
preserve
">in columnam æqualem vim poten-
<
lb
/>
tia mq́ue exercent.</
s
>
<
s
xml:id
="
echoid-s1364
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s1365
"
xml:space
="
preserve
">D*ATVM*. </
s
>
<
s
xml:id
="
echoid-s1366
"
xml:space
="
preserve
">A B columna, C D axis, E firmum, F mobile punctum eſto,
<
lb
/>
unde G obliquè extollens pondus dependeat, in ſuo ſitu columnam ſervans,
<
lb
/>
cujus obliqua linea F H. </
s
>
<
s
xml:id
="
echoid-s1367
"
xml:space
="
preserve
">Indi
<
unsure
/>
dem à puncto
<
lb
/>
<
figure
xlink:label
="
fig-527.01.044-02
"
xlink:href
="
fig-527.01.044-02a
"
number
="
76
">
<
image
file
="
527.01.044-02
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.044-02
"/>
</
figure
>
ſcilicet F, & </
s
>
<
s
xml:id
="
echoid-s1368
"
xml:space
="
preserve
">pondus I itidem obliquum,
<
lb
/>
aliovorſum depĕdeat
<
unsure
/>
, ejuſdem cum G pon-
<
lb
/>
deris, cujus obliqua linea F K, æquans K F D
<
lb
/>
angulum H F C angulo.</
s
>
<
s
xml:id
="
echoid-s1369
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s1370
"
xml:space
="
preserve
">Q*VAESITVM*. </
s
>
<
s
xml:id
="
echoid-s1371
"
xml:space
="
preserve
">Demonſtrandũ eſt pon-
<
lb
/>
deris I tantundĕ potentiæ eſſe in columnam
<
lb
/>
A B, quantum eſt ponderis G, id eſt, & </
s
>
<
s
xml:id
="
echoid-s1372
"
xml:space
="
preserve
">I
<
lb
/>
pondus (coërcito eſt amoto G) columnam
<
lb
/>
eodem in ſitu tenere.</
s
>
<
s
xml:id
="
echoid-s1373
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s1374
"
xml:space
="
preserve
">P*RAEPARATIO*. </
s
>
<
s
xml:id
="
echoid-s1375
"
xml:space
="
preserve
">Adidem punctum F, pondus L rectè extollens adda-
<
lb
/>
tur, quod non minus, in illo ſitu columnam ſuſpendat, cujus recta extol-
<
lb
/>
lens eſt F M.</
s
>
<
s
xml:id
="
echoid-s1376
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
</
text
>
</
echo
>