Valerio, Luca
,
De centro gravitatis solidorum
,
1604
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PROPOSITIO XII.
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<
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>Si hemiſphærium, vel hemiſphæroides vtcum
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que ab ſciſſum: & cylindrus, vel cylindri portio
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illi circumſcripta: & conus, vel coni portio, cu
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ius baſis eſt eadem ſolido circumſcripto, hemi
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ſphærium, vel hemiſphæroides ad verticem
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con-tingẽs
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tingens</
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, & communis axis; ſecentur vnoplano, baſi
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hemiſphærij, vel hemiſphæroidis parallelo: ſuper
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ſectiones autem prædicti coni, vel portionis coni
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cæ, & hemiſphærij, vel hemiſphæroidis, circa hu
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ius abſciſsæ portionis axem duo cylindri, vel por
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tiones cylindricæ conſtiterint; reliquum cylindri
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vel portionis cylindricæ prædicto plano abſciſsæ,
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dẽpto
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eo cylindro
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duorũ
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prædictorum, vel portio
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ne cylindrica, cuius baſis eſt ſectio hemiſphærij,
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vel hemiſphæroidis, æquale erit reliquo cylindro,
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vel portioni cylindricæ, cuius baſis eſt ſectio præ
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dicti coni, vel portionis conicæ. </
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<
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>Eſto hemiſphærium, vel hemiſphæroides ABC, cuius
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axis BD, baſis circulus, vel ellipſis, cuius diameter AC.
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>Et ſolido ABC circumſcriptus cylindrus, vel portio cy
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lindrica, cuius baſes oppoſitæ erunt circuli, vel ſimiles elli
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pſes, quarum diametri eiuſdem rationis ADC, EF, la
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tera oppoſita parallelogrammi per axem AFGC: & ſu
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per baſim, cuius diameter EF, circa axim BD, deſcriptus
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eſto conus, vel coni portio EDF. </
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<
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>Iam tria ſolida ABC,
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EDF, AC, ſecentur plano ſolidi ABC baſi parallelo,
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quod ſecabit, & ſecet vnà figuras planas per axim BD </
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