Casati, Paolo
,
Terra machinis mota : dissertationes geometricae, mechanicae physicae hydrostaticae
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ca inter eleuationes ſolidi ac depreſſiones a
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quæ analogia, præterquàm in vno caſu. </
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>Non
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quidem directa, quia, vt dicebam, KV ma
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ior eſt quàm AH, ergo maior eſt Ratio KV
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ad AG, quàm HA ad AG; atqui AG maior
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eſt quàm KN, ergo maior eſt Ratio KV ad
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KN quàm KV ad AG; ergò multò maior eſt
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Ratio KV ad KN quàm HA ad AG. </
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<
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>Noņ
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eſſe autem reciprocam analogiam ſic oſtendo. </
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XCIX
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Eleuationes
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ſolidi, &
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depreſſiones
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humidi iņ
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vaſis inæ
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qualibus
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ſunt propor
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tionales, ni ſi
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in vno caſu.
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<
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>Aqua OMRS circumfuſa eſt æqualis moli
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NL, hoc eſt VO; addatur vtrique commu
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nis moles NO, erit tota moles duobus pla
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nis KOM & NSR parallelis contenta æqualis
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moli corporis KL ſeu VS. </
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>Item aqua CDFE
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circumfuſa æqualis eſt moli GB, hoc eſt HC;
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& additâ communi mole AE, erit tota mo
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les planis ACD & GEF parallelis contentą
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æqualis moli corporis AB ſeu HE. </
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<
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>Atqui HE
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& VS æquales ſunt moles ex hypotheſi; igi
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tur & moles GD æqualis eſt moli NM: ergo
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per 34. lib. 11. baſes cum altitudinibus re
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ciprocantur, & vt AG ad KN, ita ſuperficies
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vaſis maioris ad ſuperficiem vaſis minoris. </
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<
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>Prætereà aqua circumfuſa OMRS æqua
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lis eſt moli VO, ergo ad molem KS habet
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eandem Rationem quam VO ad KS, hoc eſt
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quam altitudines KV ad KN. </
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<
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cumfuſa ad molem KS, quia in eâdem ſunt </
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