Valerio, Luca
,
De centro gravitatis solidorum
,
1604
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ter AD: & circa axim EF, ſtet cylindrus, vel portio cylin
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drica MN abſciſſa ijſdem planis cum portione ABCD
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ex cylindro, vel portione cylindrica, ſphæræ, vel ſphæroidi
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BCR circa eius axim CFSR circumſcripta, cuius ſit cen
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trum grauitatis H, ac propterea ſecta FS bifariam in pun
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cto H. reliqui autem
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dempta portione AB
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CD ex ſolido MN ſit
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centrum grauitatis K,
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quod cadet in FH, &
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portionis ABCD cen
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trum grauitatis in ipſa
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HS cadet, quod ſit L.
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<
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>Dico eſſe HK ad KL,
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vt duo rectangula GF
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R, FSE, vnà cum
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duabus tertiis quadra
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ti FS, ad quadratum
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EG. </
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ſimiliter vt ante oſtenderemus eſſe HK ad KL, vt eſt
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portio ABCD ad ſolidum MN: ſed portio ABCD
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ad ſolidum MN, eſt vt duo rectaugula GFR, ESF, vnà
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cum duabus tertiis quadrati FS, ad quadratum EG; vt
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igitur duo prædicta rectangula, vnà cum duabus tertiis
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quadrati FS ad quadratum EG, ita erit HK ad KL.
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PROPOSITIO XXXV.
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<
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>Omnis maioris portionis ſphæræ, vel ſphæroi
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dis centrum grauitatis eſt in axe, primum bifa
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riam ſecto: deinde ſecundum centrum grauitatis
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reliqui dempta portione ex cylindro, vel portione </
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