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

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="018/01/029.jpg" pagenum="21"/>
              trochleæ plurium orbiculorum conſtituan­</s>
            </p>
            <p type="main">
              <s>
                <arrow.to.target n="note15"/>
                <lb/>
              tur. </s>
              <s>Exhibeantur enim, exempli gratiâ, orbi­
                <lb/>
              culi 60, ex quibus ſi fiant 20 trochleæ trium
                <lb/>
              orbiculorum, iam ſunt decem trochlearum
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              paria, ac proinde decem Rationes vt ſum­
                <lb/>
              mum ſeptuplæ; igitur momentum potentiæ,
                <lb/>
              hoc eſt vndecimus ab vnitate terminus, eſt
                <lb/>
              vt 282475249. Si verò fiant binos haben­
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              tes orbiculos, erunt 15 trochlearum paria,
                <lb/>
              ideoq quindecim Rationes quintuplæ, ex qui­
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              bus Ratio motûs potentiæ ad motum ponde­
                <lb/>
              ris componitur; erit igitur vt 30517578125
                <lb/>
              ad 1. Conſtat autem ne additis quidem ad­
                <lb/>
              huc duobus triſpaſtorum paribus, vt ſint in
                <lb/>
              vniuerſum orbiculi 72, poſſe adeò augeri po­
                <lb/>
              tentiæ momentum: poſitis ſiquidem 12 tri­
                <lb/>
              ſpaſtorum paribus momentum potentiæ eſt
                <lb/>
              ſolùm vt 13841287201. Hinc colligitur
                <lb/>
              plus ad mouendum momenti obtinere pau­
                <lb/>
              ciores orbiculos in ſimplicioribus trochleis,
                <lb/>
              quàm in trochleis maioribus plures orbicu­
                <lb/>
              los: id quod alicui fortaſsè paradoxum ac­
                <lb/>
              cidat. </s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="note15"/>
                <emph type="italics"/>
              XIV
                <lb/>
              Pauciores
                <lb/>
              orbiculos in
                <lb/>
              ſimplicibus
                <lb/>
              trochleis
                <lb/>
              plus poſſę,
                <lb/>
              quàm plu­
                <lb/>
              res in maio­
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              ribus oſten­
                <lb/>
              ditur.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>Nunc igitur ſi mihi orbiculos centum ex­
                <lb/>
              hibeas, ſimplices trochleas ex ſingulis orbi­
                <lb/>
              culis ſtatuo, fiuntquè 50 trochlearum ſim­
                <lb/>
              plicium paria: adnexo autem pondere eidem
                <lb/>
              trochleæ, cui funis extremum alligatur, mo­</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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