Valerio, Luca
,
De centro gravitatis solidorum
,
1604
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ad cubum ex ES, triplicata eſt proportio axis, vel la
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eris BE, ad axem, vel latus ES; erit vt cubus ex BE
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ad cubum ex ES, ita ſolidum GEH ad ſolidum NEO,
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hoc eſt in eadem proportione, quæ eſt ex contraria parte ip
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ſius PR ad RQ. Cum igitur P ſit centrum grauitatis
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ſolidi NEO, & Q ſolidi GEH; erit compoſiti ex vtro
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que centrum grauitatis R. Rurſus, quoniam reliquum ſo
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lidi AH dempto hemiſphærio, vel hemiſphæroide ABC,
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æquale eſt ſolido GEH: & reliquum ſolidi TC dempto
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ſolido ALMC æquale ſolido NEO; erit vt ſolidum
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GEH ad ſolidum NEO, ideſt ex contraria parte, vt PR
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ad RQ, ita reliquum ſolidi AH dempto ABC, ad re
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liquum ſolidi TC, dempto ALMC: ſed reliqui ex ſoli
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do AH dempto ABC eſt centrum grauitatis Q: & reli
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qui ex ſolido TC dempto ALMC, centrum grauitatis
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P, ex ſuperius demonſtratis; totius igitur reliqui ex cy
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lindro, vel portione cylindrica TH dempta ſphæræ, vel
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ſphæroidis maiori portione LBM centrum grauitatis eſt
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R. </
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PROPOSITIO XXX.
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>Si ſphæra, vel ſphæroides vnà cum cylindro,
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vel portione cylindrica ipſi circumſcripta, ſece
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tur duobus planis baſi ſolidi circumſcripti pa
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rallelis, centrum intercipientibus, & ab eo non
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æqualiter diſtantibus; reliqui ex cylindro, vel
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portione cylindrica dictis planis intercepta, dem
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pta portione ſphæræ, vel ſphæroidis ipſi reſpon
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dente, centrum grauitatis eſt punctum illud, in
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quo prædicti reliqui ſolidi axis ſegmentum in</
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