DelMonte, Guidubaldo
,
Mechanicorvm Liber
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<
archimedes
>
<
text
>
<
body
>
<
chap
id
="
N13F6F
">
<
pb
n
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82
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xlink:href
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036/01/177.jpg
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<
s
id
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id.2.1.165.13.1.1.0
">Sit pondus A, ſint duo orbiculi,
<
expan
abbr
="
quorũ
">quorum</
expan
>
<
expan
abbr
="
cẽtra;
">cen
<
lb
/>
tra</
expan
>
k I trochleæ ponderi alligatæ k
<
foreign
lang
="
grc
">α</
foreign
>
; ita vt
<
lb
/>
pondus motum trochleæ ſurſum, & deorſum
<
lb
/>
ſemper ſequatur: ſit deinde orbiculus, cuius cen
<
lb
/>
trum L, trochleæ ſurſum appenſæ in
<
foreign
lang
="
el
">d</
foreign
>
; ſitq;
<
lb
/>
funis circa omnes orbiculos circumuolutus BC
<
lb
/>
DEFGHZMNO, religatuſq; in B; ſitq; po
<
lb
/>
tentia in O mouens pondus A. </
s
>
<
s
id
="
id.2.1.165.13.1.1.0.a
">dico ſpatium,
<
lb
/>
quod mouendo pertranſit potentia in O, qua
<
lb
/>
druplum eſſe ſpatii moti ponderis A. </
s
>
<
s
id
="
id.2.1.165.13.1.1.0.b
">mouean
<
lb
/>
tur orbiculi trochleæ ponderi alligatæ; & dum
<
lb
/>
centrum k eſt in R, centrum I ſit in S, & pon
<
lb
/>
dus A, hoc eſt punctum
<
foreign
lang
="
grc
">α</
foreign
>
in
<
foreign
lang
="
grc
">β</
foreign
>
: erunt IS kR
<
lb
/>
<
foreign
lang
="
grc
">αβ</
foreign
>
inter ſe ſe æquales, itemq; k I ipſi RS e
<
lb
/>
rit æqualis. </
s
>
<
s
id
="
id.2.1.165.13.1.2.0
">orbiculi enim inter ſe ſe eandem
<
lb
/>
ſemper ſeruant diſtantiam; & k
<
foreign
lang
="
grc
">α</
foreign
>
ipſi R
<
foreign
lang
="
grc
">β</
foreign
>
æ
<
lb
/>
qualis erit. </
s
>
<
s
id
="
id.2.1.165.13.1.3.0
">ducantur per orbiculorum centra
<
lb
/>
lineæ FH QT EC VX NZ horizonti æqui
<
lb
/>
diſtantes, quæ tangent funes in FHQTEC
<
lb
/>
VX NZ punctis, & inter ſe ſe quoq; æquidi
<
lb
/>
ſtantes erunt: & EQ CT VN XZ non ſo
<
lb
/>
lum inter ſe ſe, ſed etiam ipſis IS KR
<
foreign
lang
="
grc
">αβ</
foreign
>
æqua
<
lb
/>
les erunt. </
s
>
<
s
id
="
id.2.1.165.13.1.4.0
">& dum centra kI ſunt in RS, po
<
lb
/>
tentia in O ſit mota in P. </
s
>
<
s
id
="
id.2.1.165.13.1.4.0.a
">& quoniam funis
<
lb
/>
BCDEFGHZMNO eſt æqualis funi BT9
<
lb
/>
QFGHXYVP, eſt enim
<
expan
abbr
="
idẽ
">idem</
expan
>
funis, & funes cir
<
lb
/>
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figure
id
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id.036.01.177.1.jpg
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place
="
text
"
xlink:href
="
036/01/177/1.jpg
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number
="
165
"/>
<
lb
/>
ca T9Q XYV ſemicirculos ſunt æquales funibus, qui ſunt circa
<
lb
/>
CDE ZMN; Demptis igitur communibus BT, QF GHX,
<
lb
/>
& VO; erit OP æqualis ipſis VN XZ CT QE ſimul ſumptis. </
s
>
<
s
id
="
id.2.1.165.13.1.5.0
">
<
lb
/>
quatuor verò VN ZX CT QE ſunt inter ſe ſe æquales, & ſimul
<
lb
/>
quadruplæ kR, &
<
foreign
lang
="
grc
">αβ</
foreign
>
; quare OP quadrupla erit ipſius
<
foreign
lang
="
grc
">αβ</
foreign
>
. </
s
>
<
s
id
="
id.2.1.165.13.1.6.0
">ſpa
<
lb
/>
tium igitur potentiæ quadruplum eſt ſpatii ponderis. </
s
>
<
s
id
="
id.2.1.165.13.1.7.0
">quod erat
<
lb
/>
oſtendendum. </
s
>
</
p
>
<
p
id
="
id.2.1.165.14.0.0.0
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type
="
main
">
<
s
id
="
id.2.1.165.14.1.1.0
">Et ſi funis in P circa alium adhuc reuoluatur orbiculum verſus
<
lb
/>
<
foreign
lang
="
el
">d</
foreign
>
, potentia〈qué〉 mouendo ſe deorſum moueat ſurſum pondus; ſimi
<
lb
/>
liter oſtendetur ſpatium potentiæ quadruplum eſſe ſpatii ponderis. </
s
>
</
p
>
</
chap
>
</
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</
text
>
</
archimedes
>