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
List of thumbnails
<
1 - 10
11 - 20
21 - 30
31 - 40
41 - 50
51 - 60
61 - 70
71 - 80
81 - 90
91 - 100
101 - 110
111 - 120
121 - 130
131 - 140
141 - 150
151 - 160
161 - 170
171 - 180
181 - 190
191 - 197
>
71
(71)
72
(72)
73
(73)
74
(74)
75
(75)
76
(76)
77
(77)
78
79
80
<
1 - 10
11 - 20
21 - 30
31 - 40
41 - 50
51 - 60
61 - 70
71 - 80
81 - 90
91 - 100
101 - 110
111 - 120
121 - 130
131 - 140
141 - 150
151 - 160
161 - 170
171 - 180
181 - 190
191 - 197
>
page
|<
<
(122)
of 197
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div504
"
type
="
section
"
level
="
1
"
n
="
363
">
<
p
>
<
s
xml:id
="
echoid-s3529
"
xml:space
="
preserve
">
<
pb
o
="
122
"
file
="
527.01.122
"
n
="
122
"
rhead
="
4 L*IBER* S*TATICÆ*
"/>
ventio 18 propoſ. </
s
>
<
s
xml:id
="
echoid-s3530
"
xml:space
="
preserve
">inſtituitur) pondus I aquæ preſſui erit æquilibre, fundum
<
lb
/>
A C D E (ſilabi poſſe fingas) eo ſtatu conſervans.</
s
>
<
s
xml:id
="
echoid-s3531
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s3532
"
xml:space
="
preserve
">Vel, ut idem adhuc clarius illuſtrem. </
s
>
<
s
xml:id
="
echoid-s3533
"
xml:space
="
preserve
">M N O P fundum eſto, ipſi A C D E
<
lb
/>
æquale & </
s
>
<
s
xml:id
="
echoid-s3534
"
xml:space
="
preserve
">ſimile, lateribus M P, A C, M N, A E, homologis, cui inſidet ſolidum
<
lb
/>
M N O P Q ponderitate & </
s
>
<
s
xml:id
="
echoid-s3535
"
xml:space
="
preserve
">magnitudine dimidiæ
<
lb
/>
<
figure
xlink:label
="
fig-527.01.122-01
"
xlink:href
="
fig-527.01.122-01a
"
number
="
170
">
<
image
file
="
527.01.122-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.122-01
"/>
</
figure
>
columnæ A C H D E æquale ipſiq́ue ſimile, ac
<
lb
/>
recta Q O æqualis D H horizonti ad perpendi-
<
lb
/>
culum normata inſiſtat. </
s
>
<
s
xml:id
="
echoid-s3536
"
xml:space
="
preserve
">Ajo, quemadmodum ſo-
<
lb
/>
lidum M N O P Q baſin M N O P premit pon-
<
lb
/>
deroſiùs verſus N O quam ad M P, quia iſtic
<
lb
/>
corpus ipſum ſpiſſius graviuſq́ue ſit; </
s
>
<
s
xml:id
="
echoid-s3537
"
xml:space
="
preserve
">ita quoque
<
lb
/>
aquam A B ponderoſiore validioreq́ preſſu con-
<
lb
/>
niti contra E D quàm contra A C.</
s
>
<
s
xml:id
="
echoid-s3538
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s3539
"
xml:space
="
preserve
">P*RÆPARATIO*. </
s
>
<
s
xml:id
="
echoid-s3540
"
xml:space
="
preserve
">Dirimito latus A E in qua
<
unsure
/>
-
<
lb
/>
tuor quadrantes, in R, S, T, unde parallelæ ſint
<
lb
/>
R V, S X, T Y contra A C; </
s
>
<
s
xml:id
="
echoid-s3541
"
xml:space
="
preserve
">ſint item V Z, X α, Y β parallelæ contra D H,
<
lb
/>
ſecentq́ue C H in γ, δ, ε, ut quælibet eductarum γ Z, δ α, ε β æquent rectam
<
lb
/>
V γ; </
s
>
<
s
xml:id
="
echoid-s3542
"
xml:space
="
preserve
">tum ζ η per γ parallela contra C D interſecet X α in θ & </
s
>
<
s
xml:id
="
echoid-s3543
"
xml:space
="
preserve
">V β in 1, ſi-
<
lb
/>
militer Z κ per δ educta ſecet Y β in λ, ad extremum eodem ordine ducan-
<
lb
/>
tur parallelæ α μ per ε, & </
s
>
<
s
xml:id
="
echoid-s3544
"
xml:space
="
preserve
">β H per H.</
s
>
<
s
xml:id
="
echoid-s3545
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div506
"
type
="
section
"
level
="
1
"
n
="
364
">
<
head
xml:id
="
echoid-head381
"
xml:space
="
preserve
">DEMONSTRATIO.</
head
>
<
p
>
<
s
xml:id
="
echoid-s3546
"
xml:space
="
preserve
">Primùm fundo A C V R aliquod pondus incumbit, quia tuncſolum one-
<
lb
/>
re vacaret ſi in aquæ ſuperficie ſumma conſiſteret; </
s
>
<
s
xml:id
="
echoid-s3547
"
xml:space
="
preserve
">at infra eſt; </
s
>
<
s
xml:id
="
echoid-s3548
"
xml:space
="
preserve
">non igitur ponde-
<
lb
/>
ris preſſu vacat. </
s
>
<
s
xml:id
="
echoid-s3549
"
xml:space
="
preserve
">Secundò minore quàm A C ζ γ V R, aquei corporis pondere
<
lb
/>
afficitur, etenim per 10 propoſ. </
s
>
<
s
xml:id
="
echoid-s3550
"
xml:space
="
preserve
">ſi horizonti æquidiſtaret iſtud pondus ſuſtine-
<
lb
/>
ret, at nunc altiorem locum obtinet, minus igitur ſuſtinet. </
s
>
<
s
xml:id
="
echoid-s3551
"
xml:space
="
preserve
">Conſimiliter fundo
<
lb
/>
R V X S majus quoddam pondus incumbit quàm corporis A C ζ γ V R; </
s
>
<
s
xml:id
="
echoid-s3552
"
xml:space
="
preserve
">ete-
<
lb
/>
nim ſi fundum iſtud per R V horizonti æquidiſtaret iſtic per 10 propoſ. </
s
>
<
s
xml:id
="
echoid-s3553
"
xml:space
="
preserve
">tan-
<
lb
/>
tum corpus ſuſtineret: </
s
>
<
s
xml:id
="
echoid-s3554
"
xml:space
="
preserve
">at nunc cùm loco ſit inferiore plus quoq; </
s
>
<
s
xml:id
="
echoid-s3555
"
xml:space
="
preserve
">ſufferet, quam
<
lb
/>
pondus corporis A C ζ γ V S hoceſt ſibi æqualis R V γ θ X S. </
s
>
<
s
xml:id
="
echoid-s3556
"
xml:space
="
preserve
">Et rurſum mi-
<
lb
/>
nus ipſi inſidet quam corpus A C ζ θ X S, quia per 10 propof. </
s
>
<
s
xml:id
="
echoid-s3557
"
xml:space
="
preserve
">opus eſſet fun-
<
lb
/>
dum id, per S X ad horizontis paralleliſmum eductum eſſe; </
s
>
<
s
xml:id
="
echoid-s3558
"
xml:space
="
preserve
">jam verò cum fun-
<
lb
/>
dum R V X S ſublimius ſit, minus ponderis perpetitur quàm A C ζ θ X S, hoc
<
lb
/>
eſt, ipſi æquale R V Z δ X S. </
s
>
<
s
xml:id
="
echoid-s3559
"
xml:space
="
preserve
">Eodem raticinio, adhibito 10 propof. </
s
>
<
s
xml:id
="
echoid-s3560
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s3561
"
xml:space
="
preserve
">plano per
<
lb
/>
X S horizonti parallelo, cõcludes fundo S X Y T plus ponderis inſidere quàm
<
lb
/>
corporis A C ζ θ X S, hoc eſt ipſi æqualis S X δ λ Y T; </
s
>
<
s
xml:id
="
echoid-s3562
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s3563
"
xml:space
="
preserve
">minus tamen (pro-
<
lb
/>
pter eandem 10 prop. </
s
>
<
s
xml:id
="
echoid-s3564
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s3565
"
xml:space
="
preserve
">planũ per T Y horizonti parallelũ) quam A C ζ. </
s
>
<
s
xml:id
="
echoid-s3566
"
xml:space
="
preserve
">Y T
<
lb
/>
hoc eſt quam ipſi æquale S X α ε Y T. </
s
>
<
s
xml:id
="
echoid-s3567
"
xml:space
="
preserve
">Denique eadem via, ſubſidio 10 propof.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s3568
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s3569
"
xml:space
="
preserve
">plano per T Y horizonti parallelo, evincesfundo T Y D E inſidere pondus
<
lb
/>
majus corpore A C ζ. </
s
>
<
s
xml:id
="
echoid-s3570
"
xml:space
="
preserve
">Y T ſeu ipſi æquali T Y ε μ D E: </
s
>
<
s
xml:id
="
echoid-s3571
"
xml:space
="
preserve
">attamen (propter ean-
<
lb
/>
dem 10 propoſ. </
s
>
<
s
xml:id
="
echoid-s3572
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s3573
"
xml:space
="
preserve
">planum per E D horizonti parallelum) minus corpore
<
lb
/>
A C ζ η D E hoc eſt ipſo T Y β H D E. </
s
>
<
s
xml:id
="
echoid-s3574
"
xml:space
="
preserve
">Iam autem cum his demonſtrationi-
<
lb
/>
bus effectum ſit fundo A C V R aliquod pondus inſidere neque vacare omni-
<
lb
/>
no, fundo R V X S plus corpore R V γ θ X S; </
s
>
<
s
xml:id
="
echoid-s3575
"
xml:space
="
preserve
">item fundo S X Y T plus cor-
<
lb
/>
pore S X δ λ Y T, ultimùm fundo T Y D E plus corpore T Y ε μ D E, toti
<
lb
/>
quoque fundo A C D E plus inſidet quàm pondus omnium iſtorum corpo-
<
lb
/>
rum, quæ addita cõſtituunt corpus R V γ θ δ λ ε μ D E in dimidiam columnam
<
lb
/>
inſcriptum. </
s
>
<
s
xml:id
="
echoid-s3576
"
xml:space
="
preserve
">Et cum iiſdem demonſtrationibus cõcl
<
unsure
/>
uſerimus fundo A C V </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>