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 concordance
<
1 - 30
31 - 60
61 - 90
91 - 120
121 - 150
151 - 180
181 - 197
>
Scan
Original
1
2
2
3
4
4
5
5
6
6
7
7
8
8
9
9
10
10
11
11
12
12
13
13
14
14
15
15
16
16
17
17
18
18
19
19
20
20
21
21
22
22
23
23
24
24
25
25
26
26
27
27
28
28
29
29
30
30
<
1 - 30
31 - 60
61 - 90
91 - 120
121 - 150
151 - 180
181 - 197
>
page
|<
<
(13)
of 197
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div52
"
type
="
section
"
level
="
1
"
n
="
47
">
<
pb
o
="
13
"
file
="
527.01.013
"
n
="
13
"
rhead
="
*DE* S*TATICÆ ELEMENTIS*.
"/>
</
div
>
<
div
xml:id
="
echoid-div54
"
type
="
section
"
level
="
1
"
n
="
48
">
<
head
xml:id
="
echoid-head56
"
xml:space
="
preserve
">DEMONSTRATIO.</
head
>
<
head
xml:id
="
echoid-head57
"
xml:space
="
preserve
">1 MEMBRVM.</
head
>
<
p
>
<
s
xml:id
="
echoid-s274
"
xml:space
="
preserve
">MH ex dato æquatur MG. </
s
>
<
s
xml:id
="
echoid-s275
"
xml:space
="
preserve
">utrique KM addito KH æquabitur MG
<
lb
/>
& </
s
>
<
s
xml:id
="
echoid-s276
"
xml:space
="
preserve
">KM. </
s
>
<
s
xml:id
="
echoid-s277
"
xml:space
="
preserve
">ſubductoq́ue deinde hinc GK, inde KI (ex dato autem GK & </
s
>
<
s
xml:id
="
echoid-s278
"
xml:space
="
preserve
">KI
<
lb
/>
æqualia ſunt) KM & </
s
>
<
s
xml:id
="
echoid-s279
"
xml:space
="
preserve
">KM reliqua æqualia erunt IH reliquo, eorundemq́ue
<
lb
/>
dimidia æqualia fuerint.</
s
>
<
s
xml:id
="
echoid-s280
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div55
"
type
="
section
"
level
="
1
"
n
="
49
">
<
head
xml:id
="
echoid-head58
"
xml:space
="
preserve
">2 MEMBRVM.</
head
>
<
p
>
<
s
xml:id
="
echoid-s281
"
xml:space
="
preserve
">MI ad KM & </
s
>
<
s
xml:id
="
echoid-s282
"
xml:space
="
preserve
">IL addito tota ML & </
s
>
<
s
xml:id
="
echoid-s283
"
xml:space
="
preserve
">IK æqualia erunt.</
s
>
<
s
xml:id
="
echoid-s284
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div56
"
type
="
section
"
level
="
1
"
n
="
50
">
<
head
xml:id
="
echoid-head59
"
xml:space
="
preserve
">3 MEMBRVM.</
head
>
<
p
>
<
s
xml:id
="
echoid-s285
"
xml:space
="
preserve
">Vt GI ad ſui dimidium KI: </
s
>
<
s
xml:id
="
echoid-s286
"
xml:space
="
preserve
">ſic IH ad ſui dimidium IL. </
s
>
<
s
xml:id
="
echoid-s287
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s288
"
xml:space
="
preserve
">proportio-
<
lb
/>
ne alternatâ, ut GI ad IH: </
s
>
<
s
xml:id
="
echoid-s289
"
xml:space
="
preserve
">ita KI ad IL, atqui KI æquatur ML juxta 2
<
lb
/>
membrum, & </
s
>
<
s
xml:id
="
echoid-s290
"
xml:space
="
preserve
">IL ſegmento MK, juxta primum, ideoq́ue ut GI ad IH: </
s
>
<
s
xml:id
="
echoid-s291
"
xml:space
="
preserve
">ita
<
lb
/>
ML ad MK. </
s
>
<
s
xml:id
="
echoid-s292
"
xml:space
="
preserve
">Atqui ut GI ad IH: </
s
>
<
s
xml:id
="
echoid-s293
"
xml:space
="
preserve
">ita corpus five gravitas EFDA ad
<
lb
/>
EFCB, itaque ut ponderoſior gravitas EFDA, ad leviorem EFCB: </
s
>
<
s
xml:id
="
echoid-s294
"
xml:space
="
preserve
">ita
<
lb
/>
longior radius ML, ad breviorem MK.</
s
>
<
s
xml:id
="
echoid-s295
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s296
"
xml:space
="
preserve
">OCcurrerit hic non nemo. </
s
>
<
s
xml:id
="
echoid-s297
"
xml:space
="
preserve
">Propoſitionĕ deſegmentis ejuſdem columnæ,
<
lb
/>
& </
s
>
<
s
xml:id
="
echoid-s298
"
xml:space
="
preserve
">quidem æquabilis gravitatis à meeſſe demõſtratam, ignorari tamen an
<
lb
/>
veritas in aliis, & </
s
>
<
s
xml:id
="
echoid-s299
"
xml:space
="
preserve
">variis ſegmentis ſigurarum irregularium, & </
s
>
<
s
xml:id
="
echoid-s300
"
xml:space
="
preserve
">materiæ inæqua-
<
lb
/>
bilis cadem futura ſit: </
s
>
<
s
xml:id
="
echoid-s301
"
xml:space
="
preserve
">quapropter propoſitionis generalitatem ita dein-
<
lb
/>
ceps demonſtrabimus. </
s
>
<
s
xml:id
="
echoid-s302
"
xml:space
="
preserve
">Iugum KL primi modi immotum manere ima-
<
lb
/>
ginemur, ſegmentum autem EFDA demitti, lineâ è gravitatis centro edu-
<
lb
/>
ctâ ſuſpenſum è puncto K, reliquumq́ue ſe-
<
lb
/>
<
figure
xlink:label
="
fig-527.01.013-01
"
xlink:href
="
fig-527.01.013-01a
"
number
="
13
">
<
image
file
="
527.01.013-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.013-01
"/>
</
figure
>
gmentum EFCB conſimiliter depreſſum
<
lb
/>
è gravitatis centro L ſuſpendi, ſegmen-
<
lb
/>
tumq́ue EFCB ab EFDA diſtare, & </
s
>
<
s
xml:id
="
echoid-s303
"
xml:space
="
preserve
">ſi-
<
lb
/>
tum corũ eſſe qualem diagramma exhibet.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s304
"
xml:space
="
preserve
">Quando corpus primi modi ex anſa MN
<
lb
/>
penderet, ſegmenta EFCB & </
s
>
<
s
xml:id
="
echoid-s305
"
xml:space
="
preserve
">EFDA
<
lb
/>
ſitu æquipondia erant: </
s
>
<
s
xml:id
="
echoid-s306
"
xml:space
="
preserve
">neque in ſecundo
<
lb
/>
pondus EFDA depreſſius altero, plus mi-
<
lb
/>
núsve gravitatis quam in primo adſert jugo
<
lb
/>
KL, ex 3 poſtulati ſententiâ. </
s
>
<
s
xml:id
="
echoid-s307
"
xml:space
="
preserve
">Neque EFCB pondus ſecundi modi plus gra-
<
lb
/>
vitatis jugo adfert quam prius. </
s
>
<
s
xml:id
="
echoid-s308
"
xml:space
="
preserve
">Quapropter gravitates tam primi, quàm ſecun-
<
lb
/>
di modi eædem manent, jugiq́ue ſitus idem qui erat prius. </
s
>
<
s
xml:id
="
echoid-s309
"
xml:space
="
preserve
">ideoq́ue EFDA
<
lb
/>
& </
s
>
<
s
xml:id
="
echoid-s310
"
xml:space
="
preserve
">EFCB ſitu æquilibria. </
s
>
<
s
xml:id
="
echoid-s311
"
xml:space
="
preserve
">ſegmentaq́ue columnæ tam diviſa, quam conjun-
<
lb
/>
cta fitu æquipondia, atque radii eandem rationem, quam habuerunt, reti-
<
lb
/>
nent.</
s
>
<
s
xml:id
="
echoid-s312
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s313
"
xml:space
="
preserve
">Hoc probato, corpora EFDA & </
s
>
<
s
xml:id
="
echoid-s314
"
xml:space
="
preserve
">EFCB ſe-
<
lb
/>
<
figure
xlink:label
="
fig-527.01.013-02
"
xlink:href
="
fig-527.01.013-02a
"
number
="
14
">
<
image
file
="
527.01.013-02
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.013-02
"/>
</
figure
>
cundi modi aliter premendo ſingendoq́ue figure-
<
lb
/>
mus (materiam ceream, argillaceam, aliamve tra-
<
lb
/>
ctabilem eſſe ponamus) ut EFDA & </
s
>
<
s
xml:id
="
echoid-s315
"
xml:space
="
preserve
">EFCB
<
lb
/>
modi ſecundi, EFDA & </
s
>
<
s
xml:id
="
echoid-s316
"
xml:space
="
preserve
">EFCB fiant tertii;
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s317
"
xml:space
="
preserve
">KL jugum eundem poſitum ſervare, radiosq́ue
<
lb
/>
ML, & </
s
>
<
s
xml:id
="
echoid-s318
"
xml:space
="
preserve
">KM eandem rationem manifeſtum eſt,
<
lb
/>
ideoq́ue EFDA & </
s
>
<
s
xml:id
="
echoid-s319
"
xml:space
="
preserve
">EFCB ſitu æquilibria ma-
<
lb
/>
nere conſequens eſt, quia manente materiâ, muta-
<
lb
/>
tio ſormæ mutationem gravitatis non adfert.</
s
>
<
s
xml:id
="
echoid-s320
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
</
text
>
</
echo
>