Valerio, Luca
,
De centro gravitatis solidorum
,
1604
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quàm GE, ad EH; maior igitur proportio eſt GO ad
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OH, quàm GE ad EH: & componendo, maior pro
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portio GH ad HO, quàm eiuſdem GH ad HE; mi
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nor igitur OH erit quàm EH, & punctum O propin
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quius puncto D quàm punctum E; verum quoniam ex
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ijs, quæ in præcedenti libro demonſtrauimus, propoſitæ
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figuræ ſolidæ ABC centrum grauitatis eſt puncto D
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propinquius, quàm cuiuslibet figuræ ex cylindris, vel cy
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lindri portionibus æqualium altitudinum ipſi circumſcri
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ptæ, erit punctum F propinquius puncto D quàm pun
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ctum O; multo igitur puncto D erit propinquius pun
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ctum F quàm punctum E; ergo infra punctum E, & in
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linea ED cadet ſolidi ABC centrum grauitatis F.
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<
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PROPOSITIO XXV.
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>Omnis fruſti coni, vel portionis conicæ cen
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trum grauitatis eſt punctum illud, in quo eius
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axis ſic diuiditur, vt pars quæ minorem baſim at
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tingit aſſumens quartam partem axis ablati coni,
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vel portionis conicæ, ſit ad eam, quæ inter poſtre
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mam ſectionem, & quartæ partis abſciſſ<17> ad baſim
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axis totius coni terminum interijcitur, vt cubus,
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qui fit ab axe totius, ad cubum qui fit ab axe abla
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ti coni. </
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<
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>Sit coni, vel portionis conicæ ABC fruſtum BDEC,
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cuius axis FG: conus autem, vel coni portio ablata AD
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E: ſint centra grauitatis H ſolidi ABC, & K ſolidi
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ADE, & L fruſti DC: quæ centra præterquam quod </
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