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
|<
<
(129)
of 197
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div525
"
type
="
section
"
level
="
1
"
n
="
377
">
<
p
style
="
it
">
<
s
xml:id
="
echoid-s3787
"
xml:space
="
preserve
">
<
pb
o
="
129
"
file
="
527.01.129
"
n
="
129
"
rhead
="
*DE* H*YDROSTATICES ELEMENTIS*.
"/>
parallelum demiſſa. </
s
>
<
s
xml:id
="
echoid-s3788
"
xml:space
="
preserve
">Cuius cauſa hæc eſt, quod columna baſis irregularis, planoper pun-
<
lb
/>
ctain oppoſitarum baſium ambitu tranſverſim ὸμο{τα}{γῆ} (ut in columnis baſis regularis)
<
lb
/>
neceſſariò bifariam non dividatur. </
s
>
<
s
xml:id
="
echoid-s3789
"
xml:space
="
preserve
">Cæterùm ut generaliter pondus, etiam cuicunqueir-
<
lb
/>
regulari fundo inſidens cognoſcatur, Problema huiuſmodi exigimus.</
s
>
<
s
xml:id
="
echoid-s3790
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div526
"
type
="
section
"
level
="
1
"
n
="
378
">
<
head
xml:id
="
echoid-head395
"
xml:space
="
preserve
">3 PROBLEMA. 13 PROPOSITIO.</
head
>
<
p
>
<
s
xml:id
="
echoid-s3791
"
xml:space
="
preserve
">Aqueam molem ponderi fundo plano, formæ contin-
<
lb
/>
gentis inſidenti æqualem invenire.</
s
>
<
s
xml:id
="
echoid-s3792
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s3793
"
xml:space
="
preserve
">D*ATVM*. </
s
>
<
s
xml:id
="
echoid-s3794
"
xml:space
="
preserve
">A B fundum planum ſub aqua regularené an irregulare ſit nihil
<
lb
/>
intereſt. </
s
>
<
s
xml:id
="
echoid-s3795
"
xml:space
="
preserve
">Q*VAESITVM*. </
s
>
<
s
xml:id
="
echoid-s3796
"
xml:space
="
preserve
">Corpus aqueum, quod ponderi fundo A B inſi-
<
lb
/>
denti æquetur invenire.</
s
>
<
s
xml:id
="
echoid-s3797
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div527
"
type
="
section
"
level
="
1
"
n
="
379
">
<
head
xml:id
="
echoid-head396
"
xml:space
="
preserve
">CONSTRVCTIO.</
head
>
<
p
>
<
s
xml:id
="
echoid-s3798
"
xml:space
="
preserve
">Plani A B infinitè continuati & </
s
>
<
s
xml:id
="
echoid-s3799
"
xml:space
="
preserve
">ſupremæ aqueæ ſuperficiei communis ſe-
<
lb
/>
ctio eſto C, hinc fundi planique alterius & </
s
>
<
s
xml:id
="
echoid-s3800
"
xml:space
="
preserve
">horizonti & </
s
>
<
s
xml:id
="
echoid-s3801
"
xml:space
="
preserve
">fundo perpendicula-
<
lb
/>
ris communis ſectio per C, ſit C D, ipſiq́ue in plano per D horizonti paralle-
<
lb
/>
lo agatur æqualis D E quæ hujus & </
s
>
<
s
xml:id
="
echoid-s3802
"
xml:space
="
preserve
">plani per A B communi lectioni perpen-
<
lb
/>
dicularis ſit: </
s
>
<
s
xml:id
="
echoid-s3803
"
xml:space
="
preserve
">deinde plano C D E excitetur perpendiculare planũ per C & </
s
>
<
s
xml:id
="
echoid-s3804
"
xml:space
="
preserve
">E.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s3805
"
xml:space
="
preserve
">Hinc infinita A F circumagatur æquidiſtanter contra D E per ambitum fun-
<
lb
/>
<
figure
xlink:label
="
fig-527.01.129-01
"
xlink:href
="
fig-527.01.129-01a
"
number
="
179
">
<
image
file
="
527.01.129-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.129-01
"/>
</
figure
>
di A B, qua converſione deformatur corpus
<
lb
/>
A G H B a duabus infinitorum planorũ par-
<
lb
/>
tibus A B, G H & </
s
>
<
s
xml:id
="
echoid-s3806
"
xml:space
="
preserve
">ſuperficiemotu lineæ de-
<
lb
/>
ſcriptâ comprehenſum. </
s
>
<
s
xml:id
="
echoid-s3807
"
xml:space
="
preserve
">Iam ajo molem aquæ
<
lb
/>
corpori A G H Bæqualem, gravitate æquari
<
lb
/>
ponderi fundo dato inſidenti.</
s
>
<
s
xml:id
="
echoid-s3808
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s3809
"
xml:space
="
preserve
">P*RAEPARATIO*. </
s
>
<
s
xml:id
="
echoid-s3810
"
xml:space
="
preserve
">Alteram figuram prio-
<
lb
/>
ri ſimilem, æqualem, & </
s
>
<
s
xml:id
="
echoid-s3811
"
xml:space
="
preserve
">iſtiaquæ æquipondiam
<
lb
/>
figurato, hac lege ut D E horizonti ad perpendiculum immineat.</
s
>
<
s
xml:id
="
echoid-s3812
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div529
"
type
="
section
"
level
="
1
"
n
="
380
">
<
head
xml:id
="
echoid-head397
"
xml:space
="
preserve
">DEMONSTRATIO.</
head
>
<
figure
number
="
180
">
<
image
file
="
527.01.129-02
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.129-02
"/>
</
figure
>
<
p
>
<
s
xml:id
="
echoid-s3813
"
xml:space
="
preserve
">Quale pondus incumbit ſecundo fundo A B tale inſi-
<
lb
/>
det primo fundo A B, ut ſupra demonſtratum fuit, ſed
<
lb
/>
ſecundo A B inſidet pondus corporis A G H B: </
s
>
<
s
xml:id
="
echoid-s3814
"
xml:space
="
preserve
">itaque
<
lb
/>
etiam primo A B incumbit pondus æquale aqueæ moli
<
lb
/>
A G H B. </
s
>
<
s
xml:id
="
echoid-s3815
"
xml:space
="
preserve
">Quod inveniſſe & </
s
>
<
s
xml:id
="
echoid-s3816
"
xml:space
="
preserve
">demonſtraſſe fuit propoſi-
<
lb
/>
tum. </
s
>
<
s
xml:id
="
echoid-s3817
"
xml:space
="
preserve
">C*ONCLVSIO*. </
s
>
<
s
xml:id
="
echoid-s3818
"
xml:space
="
preserve
">Quamobrem aqueam molem,
<
lb
/>
ponderi fundo plano, formæ contingentis inſidenti,
<
lb
/>
æqualem invenimus. </
s
>
<
s
xml:id
="
echoid-s3819
"
xml:space
="
preserve
">Quod poſtulabatur.</
s
>
<
s
xml:id
="
echoid-s3820
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div530
"
type
="
section
"
level
="
1
"
n
="
381
">
<
head
xml:id
="
echoid-head398
"
xml:space
="
preserve
">11 THEOREMA. 14 PROPOSITIO.</
head
>
<
p
>
<
s
xml:id
="
echoid-s3821
"
xml:space
="
preserve
">Si duo parallelogramma æqualis latitudinis ab aquæ
<
lb
/>
ſumma ſuperficie deorſum æquali altitudine abdantur,
<
lb
/>
ipſorum longitudines preſsibus proportionales erunt.</
s
>
<
s
xml:id
="
echoid-s3822
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s3823
"
xml:space
="
preserve
">D*ATVM*. </
s
>
<
s
xml:id
="
echoid-s3824
"
xml:space
="
preserve
">In aqua A B C D duo parallelogramma E F, G H, æquali la-
<
lb
/>
titudine, & </
s
>
<
s
xml:id
="
echoid-s3825
"
xml:space
="
preserve
">infra aquam altitudine, hoc eſt ut perpendiculares FI, H K </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>