Stelliola, Niccol� Antonio, De gli elementi mechanici, 1597

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    <archimedes>
      <text>
        <body>
          <chap id="N105FD">
            <pb xlink:href="041/01/023.jpg" pagenum="22"/>
            <figure id="id.041.01.023.1.jpg" xlink:href="041/01/023/1.jpg" number="21"/>
            <p id="N106F0" type="head">
              <s id="N106F2">
                <emph type="italics"/>
              Dimoſtratione.
                <emph.end type="italics"/>
              </s>
            </p>
            <p id="N106F8" type="main">
              <s id="N106FA">
                <emph type="italics"/>
              Sia il vette A B, dal cui ponto D, penda il peſo C: le potenze che
                <lb/>
              ſoſtengono dette grauezze ſiano A & B: dico che'l B, e lo A ſoſten­
                <lb/>
              tano portioni proportionali all'interualli reciprocamente: cio è che
                <lb/>
              quella ragione c'ha l'interuallo, B D, a D A, quella hàbbia la por­
                <lb/>
              tione ſoſtentata dall' A, alla portione ſoſtentata dal B, ſi dimoſtra:
                <lb/>
              tagliſi ad A D uguale B E, accoppiata dunque communemente la D
                <lb/>
              E, ſarà A E uguale a B D: aggiungaſi all' A e la A G, che le ſia egua­
                <lb/>
              le, & ad E B la B F che ſimilmente le ſia eguale. </s>
              <s id="N1070C">ſarà di tutta la G F,
                <lb/>
              il ponto mezzano D, & della G E, il ponto mezzano A, & della E
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              F, il ponto mezzano B. </s>
              <s id="N10712">applicata dunque a tutta la G F, una grauez­
                <lb/>
              za che ſia uguale a C, ſarà di detta grauezza il ponto di momento in D
                <lb/>
              & ſarà equiualente nella ſua operatione alla grauezza C, & di eſſa
                <lb/>
              la parte applicata a G E ha il ſuo momento in A, c la parte applica­
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              ta ad E ha il ſuo momento in B. </s>
              <s id="N1071C">dunque della grauezza applicata
                <lb/>
              la potenza A, ne ſoſtentarà la portione applicata a G E: e la potenza
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              B, la portione applicata ad E F. </s>
              <s id="N10722">Ma G E ad E F, ha la ragione che
                <lb/>
              l'interuallo B D, a D A che è reciproca. </s>
              <s id="N10726">dunque le potenze ſoſtenta­
                <lb/>
              no le portioni de'peſi proportionali, reciprocamente pigliate con l'inter
                <lb/>
              ualli. </s>
              <s id="N1072C">ilche ſi hauea da moſtrare.
                <emph.end type="italics"/>
              </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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