Valerio, Luca
,
De centro gravitatis solidorum
,
1604
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BE bifariam in puncto R, ſecentur BD, in puncto T, &
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DE, in puncto V, bifariam & ſumatur BO, ipſius BD,
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pars quarta, necnon EP pars quarta ipſius DE, primum
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itaque quoniam ER eſt maior, quàm ED, erit punctum
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R, in ſegmento BD. </
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>Quoniam igitur ex ſupra oſtenſis O
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eſt centrum grauitatis commune cono DGH, & reliquo
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cylindri KH dempto ABC hemiſphærio: & eadem ra
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tione punctum P, cum ſit centrum grauitatis coni MDN,
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erit idem centrum grauitatis reliqui ex cylindro XL dem
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pta AKLC portione: eſt autem reliquum cylindri KH
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dempto KBL hemiſphærio, æquale cono DGH, qua
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ratione & reliquum cylindri XL, dempta AKLC por
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tione æquale eſt cono MDN; cum igitur S ſit centrum
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grauitatis totius reliqui ex toto cylindro XH, dempta
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ABC portione, erit idem S, centrum grauitatis compo
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ſiti ex conis GDH, MDL: ſunt autem horum conorum
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centra grauitatis O, P; vt igitur conus GDH, ad co
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num MDN, ita erit PS, ad SO: ſed coni GDH ad
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ſimilem ipſi conum MDN triplicata eſt proportio axis
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BD, ad axim BE, hoc eſt cylindri KH ad cylindrum
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XL; maior igitur proportio erit PS ad SO, quàm cy
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lindri KH ad cylindrum XL, ſed vt cylindrus KH, ad
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cylindrum XL, ita eſt VR ad RT, ob centra grauiratis
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V, R, T, maior igitur proportio erit PS ad SO, quàm
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VR ad RT: ſed eiuſdem PO eſt vt PD ad DO, ita
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VD ad DT, ob ſectiones axium proportionales; pun
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ctum igitur S propinquius eſt puncto O, quàm punctum
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R, per Lemma. </
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punctum R: ſed R eſt centrum grauitatis totius cylindri
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XH: & S reliqui ex cylindro XH dempta ABC por
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tione; igitur Q reliquæ portionis ABC, centrum graui
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tatis erit in linea ER, atque ideo à puncto B remotius
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quàm punctnm S. </
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<
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