Valerio, Luca
,
De centro gravitatis solidorvm libri tres
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cius minorem baſim terminatam. </
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<
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>Eſto hemiſphærio, vel hemiſphæroidi ABC, cuius axis
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BD, baſis circulus vel ellipſis, cuius diameter AC cir
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cumſcriptus cylindrus, vel cylindri portio AF, cuius in
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telligatur reliquum dempto ABC. quæ ſolida ſecans pla
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num per AC, BD, faciat ſectiones ſemicirculum, vel ſe
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miellipſim ABC, & parallelogrammum per axem AE
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FC; & per quodlibet punctum L axis BD, planum baſibus
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AC, EF ſolidi AF
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parallelũ
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, ſecans prædicta ſolida ABC,
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AF, faciat ſectiones circulos, vel ellipſes ſimiles, & in ſolido
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AF etiam æquales ijs, quæ circa AC, EF: earum autem dia
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metros, ſectiones cum
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parallelogrãmo
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AEFC, ipſam GO:
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& cum ſemicirculo, vel ſemiellipſe ABC, ipſam HN. </
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<
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que habebimus figuram quandam ſolidam GHBNO reſi
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duum cylindri, vel portionis cylindricæ GF dempta mino
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ri ſphæræ, vel ſphæroidis portione HBN, cuius axis erit BL.
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>Sumpta igitur BQ quarta parte axis BD, & LP quarta par
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te ipſius DL fiat vt cu
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bus ex BD ad cubum ex
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DL, ita PR ad
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Rq.
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Dico reſidui GHBNO
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centrum grauitatis eſſe
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R. </
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<
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cylindro, vel portione
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cylindrica AO dempta
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portione AHNC, cen
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trum grauitatis eſſe P.
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Nam ſuper baſim circulum, vel ellipſim EF, ſtet conus, vel
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portio conica EDF: ſitque prædicto plano per L abſciſ
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ſus conus, vel coni portio KDM, cuius axis DL, quæ pro
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pter planum ſecans baſi EF parallelum, ſimilis erit toti
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cono, vel portioni conicæ EDF. </
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<
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eſt axis BD pars quarta, & LP pars quarta ipſius DL; </
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