Casati, Paolo, Terra machinis mota : dissertationes geometricae, mechanicae physicae hydrostaticae

Table of figures

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              perficiem minoris: ſed vt VK ad HA, itą
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              moles VO ad molem HC, hoc eſt aquą
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              OMRS ad aquam CDFE; ergo vt ſuperficies
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              vaſis maioris ad ſuperficiem minoris, hoc eſt
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              vt GA ad NK, ita aqua OMRS ad aquam̨
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              CDFE. </s>
              <s>Atqui aquæ iſtæ circumfuſæ habent
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              Rationem compoſitam ex Rationibus altitu­
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              dinum & baſium; ergo Ratio GA ad NK
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              æqualis eſt
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              R
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              ationi compoſitæ
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              ex Rationi­
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              bus altitudinum GA ad N
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              K,
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              & baſium CD
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              ad OM. </s>
              <s>Cum verò fieri non poſſit vt (quan­
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              do Ratio non componitur ex duabus Ratio­
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              nibus, quarum altera ſit alterius ſubduplica­
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              ta, vt Ratio compoſita ex Rationibus 4 ad 2
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              & 2 ad 8, eſt eadem cum Ratione 2 ad 4
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              conuerſa prions Rationis 4 ad 2, quemad­
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              modum hic non contingere ſuppono) Ratio
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              aliqua compoſita eadem ſit directè cum vnâ
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              ex Rationibus componentibus, niſi alterą
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              Ratio componens ſit Ratio æqualitatis (ſic
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              Ratio compoſita ex Rationibus 4 ad 4 & 4 ad
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              3 eſt 16 ad 12 eadem cum Ratione 4 ad 3,
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              quia Ratio æqualitatis aliam Rationem mul­
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              tiplicans eam non mutat) conſtet autem ex
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              demonſtratis AG maiorem eſſe quàm KN,
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              ſequitur baſes aquarum CD & OM haberę
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              Rationem æqualitatis. </s>
              <s>At baſes iſtæ ſunt ſu­
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              perficies vaſorum minùs ſuperficie ſolidi im­</s>
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