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

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              <s>
                <pb xlink:href="018/01/228.jpg" pagenum="214"/>
              cie ſolidi. </s>
              <s>Igitur ſuperficies ſolidi eſt medio
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              loco proportionalis inter differentias, quibus
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              ſuperficies ſolidi exceditur à ſuperficiebus va­
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              ſorum: ergo componendo & permutando vt
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              ſuperficies vaſis maioris ad ſuperficiem mi­
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              noris, ita ſuperficies ſolidi HT ad ſuperficiem
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              vaſis minoris minùs ſuperficie ſolidi, hoc eſt
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              ſuperficiem aquæ CD. </s>
              <s>Sed vt ſuperficies ſo­
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              lidi HT ad ſuperficiem CD, ita moles AE
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              ad aquam CDFE eiuſdem altitudinis: & quia
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              AG ex hypotheſi eſt æqualis ipſi VK, moles
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              AE eſt æqualis ipſi moli VO, hoc eſt aquæ
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              OMRS. ergo vt ſuperficies HT ad ſuperfi­
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              ciem CD, ita aqua OMRS ad aquam CDFE;
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              ergo per 11. 5. vt ſuperficies vaſis maioris ad
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              ſuperficiem minoris, hoc eſt vt aquarum al­
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              titudines AG ad KN, ita aqua OMRS ad a­
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              quam CDFE. </s>
              <s>Sunt igitur aquæ inter ſe re­
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              ciprocè vt earum altitudines: Ratio autem̨
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              molium ex Rationibus altitudinum &
                <expan abbr="baſiũ">baſium</expan>
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              componitur, baſes verò non habent rationem
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              æqualitatis; ergo aquarum ſuperficies OM
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              ad CD ſunt in duplicatâ Ratione altitudinum
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              reciprocè ſumptarum, hoc eſt vt quadratum̨
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              GA ad quadratum KN. </s>
              <s>Id quod ſic breui­
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              ter demonſtro Algebricis notis. </s>
            </p>
            <p type="main">
              <s>Sit GA altitudo R, & KN altitudo ſit S:
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              ſuperficies CD ſit D planum, & ſuperficies </s>
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