Commandino, Federico
,
Liber de centro gravitatis solidorum
,
1565
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023/01/023.jpg
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<
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id
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s.000215
">æquidiſtant autem cgo, mnp. </
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>
<
s
id
="
s.000216
">ergo
<
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abbr
="
parallelogrãma
">parallelogramma</
expan
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ſunt
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lb
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on, gm, & linea mn æqualis cg; & np ipſi go. </
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>
<
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id
="
s.000217
">aptatis igi
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tur klm, abc
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expan
abbr
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triãgulis
">triangulis</
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>
, quæ æqualia & ſimilia
<
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abbr
="
sũt
">sunt</
expan
>
; linea mp
<
lb
/>
in co, & punctum n in g cadet. </
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>
<
s
id
="
s.000218
">Quòd
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abbr
="
cũ
">cum</
expan
>
g ſit centrum gra
<
lb
/>
uitatis trianguli abc, & n trianguli klm grauitatis cen
<
lb
/>
trum erit id, quod demonſtrandum relinquebatur. </
s
>
<
s
id
="
s.000219
">Simili
<
lb
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ratione idem contingere demonſtrabimus in aliis priſma
<
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tibus, ſiue quadrilatera, ſiue plurilatera habeant plana,
<
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quæ opponuntur.</
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16. unde
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cimi</
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34. primi</
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10. unde
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cimi</
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10. unde
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cimi</
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id
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4. ſexti</
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type
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<
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id
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">
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per 5. pe
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titionem
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Archime
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dis.</
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>
</
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<
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type
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">
<
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id
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">COROLLARIVM.</
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type
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<
s
id
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">Ex iam demonſtratis perſpicue apparet, cuius
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/>
libet priſmatis axem, parallelogrammorum lateri
<
lb
/>
bus, quæ ab oppoſitis planis
<
expan
abbr
="
ducũtur
">ducuntur</
expan
>
æquidiſtare.</
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>
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<
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id
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">THEOREMA VI. PROPOSITIO VI.</
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>
</
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<
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type
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<
s
id
="
s.000229
">Cuiuslibet priſmatis centrum grauitatis eſt in
<
lb
/>
plano, quod oppoſitis planis æquidiſtans, reli
<
lb
/>
quorum planorum latera bifariam diuidit.</
s
>
</
p
>
<
p
type
="
main
">
<
s
id
="
s.000230
">Sit priſma, in quo plana, quæ opponuntur ſint trian
<
lb
/>
gula ace, bdf: & parallelogrammorum latera ab, cd,
<
lb
/>
ef bifariam
<
expan
abbr
="
diuidãtur
">diuidantur</
expan
>
in punctis ghk: per diuiſiones au
<
lb
/>
<
arrow.to.target
n
="
marg30
"/>
<
lb
/>
tem planum ducatur; cuius ſectio figura ghK. </
s
>
<
s
id
="
s.000231
">erit linea
<
lb
/>
gh æquidiſtans lineis ac, bd & hk ipſis ce, df. </
s
>
<
s
id
="
s.000232
">quare ex
<
lb
/>
decimaquinta undecimi elementorum, planum illud pla
<
lb
/>
nis ace, bdf æquidiſtabit, & faciet ſectionem figu
<
lb
/>
<
arrow.to.target
n
="
marg31
"/>
<
lb
/>
ram ipſis æqualem, & ſimilem, ut proxime demonſtra
<
lb
/>
uimus. </
s
>
<
s
id
="
s.000233
">Dico centrum grauitatis priſmatis eſſe in plano
<
lb
/>
ghk. </
s
>
<
s
id
="
s.000234
">Si enim fieri poteſt, ſit eius centrum l: & ducatur
<
lb
/>
lm uſque ad planum ghk, quæ ipſi ab æquidiſtet. </
s
>
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