Valerio, Luca
,
De centro gravitatis solidorum
,
1604
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PROPOSITIO XXXVII.
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<
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>Dodecaedri, & icoſaedri idem eſt centrum gra
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uitatis, & figuræ. </
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<
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>Nam huiuſmodi figuras habere axes, qui omnes ſe ſe
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bifariam ſecant; (tale autem ſectionis punctum centrum eſt)
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conſtat ex talium corporum in ſphæra inſcriptione in de
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cimotertio Euclidis Elemento: nec non omnem pyrami
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dem, cuius vertex eſt dodecaedri, vel octaedri centrum
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idem cum centro ſphæræ, vt conſtat ex ijſdem Euclidis in
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ſcriptionibus; baſis autem triangulum æquilaterum, vel
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pentagonum, vna ex baſibus corporum prædictorum, ha
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bere pyramidem oppoſitam ſimilem ipſi, & æqualem, cuius
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latera eius lateribus homologis ſunt in directum poſita,
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baſis autem triangulum, vel pentagonum, quale diximus;
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Eadem igitur ratione, qua vſi ſumus ad demonſtrandum
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centrum grauitatis, & parallelepipedi, & octaedri, propo
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ſitum concluderemus. </
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PROPOSITIO XXXVIII.
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<
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>Data qualibet figura, cuius termini omnis
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cauitas ſit interior, ſi certum in ea punctum talis
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cius partis centrum grauitatis eſse poſsit, quæ ab
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ca deficiat minori ſpacio quantacumque magnitu
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dine propoſita; illud erit totius figuræ centrum
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grauitatis. </
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