Commandino, Federico
,
Liber de centro gravitatis solidorum
,
1565
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45
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ad punctum
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grc
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Sed quoniam
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circumſcripta itidem alia
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figura æquali interuallo ad portionis centrum accedit, ubi
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primum
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applicuerit ſe ad
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&
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ad
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abbr
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punctũ
">punctum</
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<
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="
grc
">ψ,</
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hoc eſt ad
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portionis centrum ſe applicabit. </
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>
<
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id
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s.000940
">quod fieri nullo modo
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poſſe perſpicuum eſt. </
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>
<
s
id
="
s.000941
">non aliter idem abſurdum ſequetur,
<
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/>
fi ponamus centrum portionis recedere à medio ad par
<
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/>
tes
<
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lang
="
grc
">ω;</
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eſſet enim aliquando centrum figuræ inſcriptæ idem
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quod portionis
<
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abbr
="
centrũ
">centrum</
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>
. </
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>
<
s
id
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s.000942
">ergo punctum e centrum erit gra
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uitatis portionis abc. quod demonſtrare oportebat.</
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7. huius</
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8. primi
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libri Ar
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chimedis</
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11. duo
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decimi.</
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15. quinti</
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2. duode
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cimi</
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20. primi
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<
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abbr
="
conicorũ
">conicorum</
expan
>
</
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>
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19.
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quinti</
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">
<
s
id
="
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">Quod autem ſupra
<
expan
abbr
="
demõſtratum
">demonſtratum</
expan
>
eſt in portione conoi
<
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/>
dis recta per figuras, quæ ex cylindris æqualem altitudi
<
lb
/>
dinem habentibus conſtant, idem ſimiliter demonſtrabi
<
lb
/>
mus per figuras ex cylindri portionibus conſtantes in ea
<
lb
/>
portione, quæ plano non ad axem recto abſcinditur. </
s
>
<
s
id
="
s.000951
">ut
<
lb
/>
enim tradidimus in commentariis in undecimam propoſi
<
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/>
tionem libri Archimedis de conoidibus & ſphæroidibus. </
s
>
<
lb
/>
<
s
id
="
s.000952
">portiones cylindri, quæ æquali ſunt altitudine eam inter ſe
<
lb
/>
ſe proportionem habent, quam ipſarum baſes: baſes
<
expan
abbr
="
autẽ
">autem</
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>
<
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/>
<
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n
="
marg110
"/>
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quæ ſunt ellipſes ſimiles eandem proportionem habere,
<
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quam quadrata diametrorum eiuſdem rationis, ex corol
<
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/>
lario ſeptimæ propoſitionis libri de conoidibus, & ſphæ
<
lb
/>
roidibus, manifeſte apparet.</
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>
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corol. 15
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de conoi
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dibus &
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ſphæroi
<
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dibus.</
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>
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<
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">
<
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id
="
s.000954
">THEOREMA XXIIII. PROPOSITIO XXX.</
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>
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>
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">
<
s
id
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">Si à portione conoidis rectanguli alia portio
<
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abſcindatur, plano baſi æquidiſtante; habebit
<
lb
/>
portio tota ad eam, quæ abſciſſa eſt, duplam pro
<
lb
/>
portion em eius, quæ eſt baſis maioris portionis
<
lb
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ad baſi m minoris, uel quæ axis maioris ad axem
<
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minoris.</
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>
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