DelMonte, Guidubaldo, Le mechaniche

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    <archimedes>
      <text id="id.0.0.0.0.3">
        <body id="id.2.0.0.0.0">
          <chap id="N14EBE">
            <p id="id.2.1.916.0.0" type="main">
              <s id="id.2.1.916.2.0">
                <pb pagenum="79" xlink:href="037/01/173.jpg"/>
                <emph type="italics"/>
              infinito ſi troueranno le proportioni dello ſpatio della poſſanza allo ſpatio del pe­
                <lb/>
              ſo moſſo quanto ſi vogliano moltiplici.
                <emph.end type="italics"/>
              </s>
            </p>
            <p id="id.2.1.917.0.0" type="main">
              <s id="id.2.1.917.1.0">Et coſi procedendo in infinito ſi troueranno le proportioni dello ſpatio della poſ­
                <lb/>
              ſanza allo ſpatio del peſo moſſo quanto ſi vorrà moltiplici. </s>
              <s id="id.2.1.917.2.0">Già è detto che mol
                <lb/>
              tiplice è il primo genere delle proportioni nelle quantità paragonate dal mag­
                <lb/>
              giore al minore, però qui vuol dire, che con tale regola ſi ritroueranno le pro­
                <lb/>
              portioni dello ſpatio del peſo allo ſpatio della poſſanza in infinito,
                <expan abbr="douẽdo">douendo</expan>
              eſſere
                <lb/>
              lo ſpatio della poſſanza mouente moltiplice, cioè molte volte maggiore dello
                <lb/>
              ſpatio del peſo moſſo, come appare nel preſente eſſempio, che è ſei volte più,
                <lb/>
              come ſei ad vno; & queſto è il ſignificato di moltiplice. </s>
            </p>
            <p id="id.2.1.918.0.0" type="head">
              <s id="id.2.1.918.1.0">COROLLARIO I. </s>
            </p>
            <p id="id.2.1.919.0.0" type="main">
              <s id="id.2.1.919.1.0">Da queſte coſe è manifeſto, coſi hauerſi il peſo verſo la poſſan­
                <lb/>
              za, che lo ſoſtiene, come lo ſpatio della poſſanza che moue al­
                <lb/>
              lo ſpatio del peſo moſſo. </s>
            </p>
            <p id="id.2.1.920.0.0" type="main">
              <s id="id.2.1.920.1.0">
                <emph type="italics"/>
              Come ſe il peſo A ſarà cinque volte tanto quanto la poſſanza di O, che ſoſtiene
                <lb/>
              il detto peſo A; ſarà anche lo ſpatio OP della poſſanza mouente il peſo cin­
                <lb/>
              que volte tanto quanto lo ſpatio
                <foreign lang="grc">α β</foreign>
              del peſo moſſo.
                <emph.end type="italics"/>
              </s>
            </p>
            <p id="id.2.1.921.0.0" type="head">
              <s id="id.2.1.921.1.0">COROLLARIO II. </s>
            </p>
            <p id="id.2.1.922.0.0" type="main">
              <s id="id.2.1.922.1.0">E manifeſto ancora per le coſe dette, che le girelle della taglia,
                <lb/>
              laquale è legata al peſo, fanno sì, che minore ſpatio è quello,
                <lb/>
              ilquale è deſcritto dal peſo moſſo, che dalla poſſanza che tira;
                <lb/>
              & che in tempo maggiore ſi deſcriua vn dato ſpatio eguale,
                <lb/>
              che ſenza loro: ilche veramente non fanno le girelle della ta­
                <lb/>
              glia di ſopra. </s>
            </p>
            <p id="id.2.1.923.0.0" type="main">
              <s id="id.2.1.923.1.0">
                <emph type="italics"/>
              Moſtrata la proportione moltiplice, che ha il peſo verſo la poſſanza, hora ſi moſtri per
                <lb/>
              lo contrario la proportione moltiplice, che haue la poſſanza verſo il peſo.
                <emph.end type="italics"/>
              </s>
            </p>
            <p id="id.2.1.924.0.0" type="head">
              <s id="id.2.1.924.1.0">PROPOSITIONE XV. </s>
            </p>
            <p id="id.2.1.925.0.0" type="main">
              <s id="id.2.1.925.1.0">Se la corda ſarà inuolta d'intorno alla girella della taglia tenu­
                <lb/>
              ta di ſopra dalla poſſanza; l'vn capo dellaquale ſia legato in
                <lb/>
              qualche loco, ma all'altro ſia appiccato il peſo, ſarà la poſſan­
                <lb/>
              za due volte tanto quanto il peſo. </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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