DelMonte, Guidubaldo
,
Mechanicorvm Liber
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<
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id
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N128CF
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036/01/098.jpg
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<
s
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id.2.1.85.8.1.1.0
">Sit vectis AB, cuius ful
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lb
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cimentum C; & ex puncto B
<
lb
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ſit pondus D ſuſpenſum; ſitq;
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lb
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potentia in A mouens pon
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lb
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dus D vecte AB. </
s
>
<
s
id
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id.2.1.85.8.1.1.0.a
">Dico ſpa
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lb
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tium potentiæ in A ad ſpa
<
lb
/>
tium ponderis ita eſſe, vt CA
<
lb
/>
ad CB. </
s
>
<
s
id
="
id.2.1.85.8.1.1.0.b
">Moueatur vectis AB,
<
lb
/>
& vt pondus D ſurſum mo
<
lb
/>
ueatur, oportet B ſurſum mo
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lb
/>
ueri, A verò deorſum. </
s
>
<
s
id
="
id.2.1.85.8.1.2.0
">& quo
<
lb
/>
niam C eſt punctum immobi
<
lb
/>
le; idcirco dum A, & B mo
<
lb
/>
uentur,
<
expan
abbr
="
circulorũ
">circulorum</
expan
>
circumferen
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lb
/>
tias deſcribent. </
s
>
<
s
id
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id.2.1.85.8.1.3.0
">Moueatur igi
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lb
/>
tur AB in EF; erunt AE
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lb
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<
lb
/>
BF circulorum circumferentiæ, quorum ſemidiametri ſunt CA
<
lb
/>
CB. </
s
>
<
s
id
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N12D91
">tota compleatur circumferentia AGE, & tota BHF; ſintq;
<
lb
/>
KH puncta, vbi AB, & EF circulum BHF ſecant. </
s
>
<
s
id
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id.2.1.85.8.1.4.0
">Quoniam e
<
lb
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n
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nim angulus BCF eſt æqualis angulo HCk; erit circumferentia
<
lb
/>
<
arrow.to.target
n
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note140
"/>
kH circumferentiæ BF æqualis. </
s
>
<
s
id
="
id.2.1.85.8.1.5.0
">cùm autem circumferentiæ AE
<
lb
/>
kH ſint ſub eodem angulo ACE, & circumferentia AE ad to
<
lb
/>
tam circumferentiam AGE ſit, vt angulus ACE ad quatuor re
<
lb
/>
ctos; vt autem idem angulus HCk ad quatuor rectos, ita quoq;
<
lb
/>
eſt circumferentia HK ad totam circumferentiam HBK; erit cir
<
lb
/>
cumferentia AE ad totam circumferentiam AGE, vt circumfe
<
lb
/>
<
arrow.to.target
n
="
note141
"/>
rentia kH ad totam kFH. </
s
>
<
s
id
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id.2.1.85.8.1.5.0.a
">& permutando, vt circumferentia
<
lb
/>
AE ad circumferentiam kH, hoc eſt BF, ita tota circumferen
<
lb
/>
tia AGE ad totam circumferentiam BHF. </
s
>
<
s
id
="
id.2.1.85.8.1.5.0.b
">tota verò circumfe
<
lb
/>
rentia AGE ita ſe habet ad totam BHF, vt diameter circuli AEG
<
lb
/>
<
arrow.to.target
n
="
note142
"/>
ad diametrum circuli BHF. </
s
>
<
s
id
="
id.2.1.85.8.1.5.0.c
">Vt igitur circumferentia AE ad cir
<
lb
/>
<
arrow.to.target
n
="
note143
"/>
cumferentiam BF, ita diameter circuli AGE ad diametrum cir
<
lb
/>
culi BHF: vt autem diameter ad diametrum, ita ſemidiameter
<
lb
/>
ad ſemidiametrum, hoc eſt CA ad CB: quare vt circumferen
<
lb
/>
tia AE ad circumferentiam BF, ita CA ad CF. </
s
>
<
s
id
="
N12DD0
">circumferentia
<
lb
/>
verò AE ſpatium eſt potentiæ motæ, & circumferentia BF eſt </
s
>
</
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</
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