Baliani, Giovanni Battista
,
De motv natvrali gravivm solidorvm et liqvidorvm
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">PROPOSITIO TERTIA</
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">Lineae descensus gravium, dum naturali motu
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perpendiculariter feruntur, sunt in dupliĀ
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cata ratione diuturnitatum.
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4
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type
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proof
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<
s
id
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">Sint LN, KM linea descensus gravium L, K,
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& sint PO ipsorum diuturnitates.</
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">Dico LN, KM esse in duplicata ratione ipsarum P, O.</
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">Sint pendula AH, AI, dependentia a puncto A, &
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eleventur ad libellam ipsius A usque ad E, B,
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quae in elevatione producant arcus HB, IE, &
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sint talis longitudinis, ut ducta ACF, secet arĀ
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cus BC, & EF, tam parvae curvitatis ut pro
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rectis habeantur, puta portionis minimae, &
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proinde aequales quo ad sensum rectis KM, LN,
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& fiat V tertia proportionalis ad O, P,
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Per 3 pet.</
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Per 11 sexti.</
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<
s
id
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">Quoniam O, P sunt diuturnitates KM, LN ex
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constr., sunt itidem diuturnitates BC, EF,
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&
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quia diuturnitates vibrorum AH, AI sunt
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etiam ut O ad P
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AH AI sunt ut O, ad V
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& pariter BC, & EF sunt ut O ad V
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Ergo
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KM, LN eis aequales per constr. sunt etiam ut
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O ad V, & proinde in duplicata ratione O, P,
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temporum seu diuturnitatum earumdem. </
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<
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Per 5 pet.</
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Per 3 supp.</
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