Casati, Paolo
,
Terra machinis mota : dissertationes geometricae, mechanicae physicae hydrostaticae
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OM ſit Z planum. </
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<
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>lgitur aqua CDEF eſt
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D plan. in R; & aqua OMRS eſt Z plan; iņ
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S. </
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<
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>Quare cum ſit Z plan. in S ad D plan. in R,
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vt R ad S. erit per 16. 6. vel 19. 7. Z pl. </
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<
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>in S.
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quadr. </
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<
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>æquale D plano in R quadratum: ‘er
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go Z planum ad D planum, hoc eſt ſuperfi
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cies OM ad ſuperficiem CD, eſt vt R qua
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dratum ad S quadratum: ſunt igitur ſuperfi
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cies aquarum in duplicatâ Ratione altitudi
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num AG ad KN. </
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<
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>At in Ratione AG ad KN
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eſt ſuperficies vaſis maioris ad ſuperficiem̨
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minoris, ergo ſuperficies OM ad ſuperficiem
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CD eſt in duplicatâ Ratione ſuperficiei vaſis
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maioris ad ſuperficiem minoris. </
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<
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>Datis itaque vaſis ſimilibus inæqualibus,
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& datâ Ratione ſuperficierum huiuſmodi va
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ſorum, poterimus reperire ſuperficiem ſoli
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di VY aut HT; quæ ex vaſorum ſuperficie
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bus dempta reliquam aquæ ſuperficiem relin
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quat in duplicatâ Ratione ſuperficierum va
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ſorum. </
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<
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>Cum enim ſolidorum ſuperficies HT,
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VY habeant Rationem æqualitatis, maior eſt
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Ratio totius ſuperficiei vaſis maioris ad totam
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ſuperficiem minoris, quàm ablatæ VY ad
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ablatam HT, ergo per 33 5. apud Clau. ma
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ior eſt Ratio reliquæ OM ad reliquam CD,
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quàm totius ad totam: quare poteſt etiam̨
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haberi Ratio duplicata Rationis totius ad to</
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