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">
            <pb xlink:href="037/01/138.jpg"/>
            <p id="id.2.1.770.0.0" type="head">
              <s id="id.2.1.770.1.0">PROPOSITIONE IIII. </s>
            </p>
            <p id="id.2.1.771.0.0" type="main">
              <s id="id.2.1.771.1.0">Sia la leua AB, il cui ſoſtegno ſia A, laqual leua ſia diuiſa in
                <lb/>
              due parti eguali in D, & ſia il peſo C appiccato in D, &
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              ſiano due poſſanze eguali in BD, che ſoſtengano il peſo C.
                <lb/>
              </s>
              <s id="id.2.1.771.2.0">Dico, che ogn'vna di queſte poſſanze poſte in BD è vn ter­
                <lb/>
              zo del peſo C. </s>
            </p>
            <p id="id.2.1.772.0.0" type="main">
              <s id="id.2.1.772.1.0">
                <emph type="italics"/>
              Hor percioche vna delle due poſſanze è collocata in D, & il peſo C ſtà appiccato
                <lb/>
              all'iſteſſo punto D. </s>
              <s id="id.2.1.772.2.0">La poſſanza in D ſoſienirà la parte del peſo C, che ſarà
                <lb/>
              eguale ad eſſa poſſan­
                <lb/>
              za D. </s>
              <s id="id.2.1.772.3.0">Per laqual co
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              ſala poſſanza in B ſo
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              ſtenirà l'altra parte re
                <lb/>
              ſtante, laqual parte ſa
                <lb/>
              rà il doppio
                <expan abbr="tāto">tanto</expan>
              , quan
                <lb/>
              to è la poſſanza di B,
                <lb/>
              eſſendo che il peſo ver
                <lb/>
              ſo la poſſanza ha la
                <lb/>
              proportione iſteſſa, che
                <emph.end type="italics"/>
                <lb/>
                <figure id="id.037.01.138.1.jpg" xlink:href="037/01/138/1.jpg" number="135"/>
                <lb/>
                <emph type="italics"/>
              ha AB ad AD: & le poſſanze poſte in BD ſono eguali, adunque la poſ­
                <lb/>
              ſanza, che è in B ſoſtenirà il doppio più di quello, che ſoſtenirà la poſſanza, che è
                <lb/>
              in D. </s>
              <s id="id.2.1.772.4.0">Diuidaſi dunque il peſo C in due parti, l'vna delle quali ſia il doppio del­
                <lb/>
              l'altra: ilche ſi farà, ſe lo diuideremo in tre parti eguali EFG, & all'hora FG
                <lb/>
              ſarà il doppio di E. </s>
              <s id="id.2.1.772.5.0">Coſi la poſſanza in D ſoſtenirà la parte E, & la poſſanza
                <lb/>
              in B le altre due parti FG. </s>
              <s id="id.2.1.772.6.0">Ambedue dunque le poſſanze poſte in BD tra
                <lb/>
              loro eguali
                <expan abbr="ſoſterrãno">ſoſterranno</expan>
              inſieme tutto il peſo C. </s>
              <s id="N15424">& perche la poſſanza in D ſoſtie­
                <lb/>
              ne la parte E, laquale è la terza parte del peſo C, & ad eſſo è eguale, ſarà la poſ­
                <lb/>
              ſanza in D vn terzo del peſo C: & concioſia che la poſſanza di B ſoſtenga le
                <lb/>
              parti FG, la poſſanza dellequali poſta in B è la metà meno: ſarà la poſſanza
                <lb/>
              in B all'vna delle parti FG, come alla G eguale. </s>
              <s id="id.2.1.772.7.0">& il G è la terza parte
                <lb/>
              del peſo C. </s>
              <s id="id.2.1.772.8.0">La poſſanza dunque in B ſarà il terzo del peſo C. </s>
              <s id="id.2.1.772.9.0">Ciaſcuna delle
                <lb/>
              poſſanze dunque in BD è vn terzo del peſo C, che biſognaua dimoſtrare.
                <emph.end type="italics"/>
              </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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