Valerio, Luca
,
De centro gravitatis solidorum
,
1604
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LEMMA.
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Sit data recta PO, & in ea punctum D, & punctum quod
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dam R in ipſa DO, ita vt VD ipſius PD, ad DT ipſius DO,
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ſit vt PD, ad DO: ſit autem maior proportio PS ad SO, quàm
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VR, ad RT. </
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<
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>Dico OS, minorem eſſe quàm OR.
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>Fiat enim vt PS, ad SO, ita VZ ad ZT; ma
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ìor igitur erit proportio VZ, ad ZT, quàm VR, ad
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RT: & componendo maior proportio VT, ad TZ,
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quàm VT, ad TR; minor igitur TZ, quàm TR, ideſt
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maior DZ, quàm DR. </
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>Rurſus quia componendo eſt
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vt PO ad OS, ita VT ad TZ: ſed vt DO ad OP, ita
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eſt DT ad TV; erit ex æquali, vt DO ad OS, ita DT,
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ad TZ; & per conuerſionem rationis, vt OD ad DS,
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ita TD ad DZ: & permutando, vt DO ad DT, ita DS
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ad DZ: ſed DO, eſt maior quàm DT, ergo & DS, erit
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maior quàm DZ: ſed DZ maior erat quàm DR; multo
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ergo DS maior quàm DR, vnde minor erit OS quàm
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OR. </
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<
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>Quod demonſtrandum erat. </
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PROPOSITIO XXXVII.
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<
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>Si datæ maiori ſphæræ portioni cylindrus cir
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cumſcribatur circa eundem axim portionis, cen
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trum grauitatis reliquæ figuræ ex cylindro cir
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cumſcripto ablata portione, propinquius erit ver
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tici portionis, quàm
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grauitatis portionis. </
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