DelMonte, Guidubaldo, In duos Archimedis aequeponderantium libros Paraphrasis : scholijs illustrata

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    <archimedes>
      <text>
        <body>
          <chap id="N10019">
            <p id="N1196C" type="main">
              <s id="N11A1D">
                <pb xlink:href="077/01/050.jpg" pagenum="46"/>
              tes ex determinatis diſtantijs determinatas quo〈que〉 habeant
                <lb/>
              grauitates; ſi ex dato puncto æ〈que〉ponderare debent. </s>
              <s id="N11A25">Quòd
                <lb/>
              ſi in hoc caſu datum fuerit punctum C, ex quo pondera AB
                <lb/>
              ex æqualibus diſtantijs CA CB ę〈que〉ponderare debeant: o­
                <lb/>
              porteret, vt pondera AB (ex demonſtratis) ſemper eſſent æ­
                <lb/>
              qualia.
                <expan abbr="Quoniã">Quoniam</expan>
                <expan abbr="autẽ">autem</expan>
                <expan abbr="quomodocũ〈que〉">quomodocun〈que〉</expan>
              ſint pondera, hoc eſt; ſi
                <lb/>
              ue pondus A maius, ſiue minus fuerit, quàm B, manent, ſi
                <lb/>
              igitur dixerimus, ergo pondus A ponderi B ę〈que〉ponderat;
                <lb/>
              eſſet omnino inconueniens. </s>
              <s id="N11A41">cùm ex ijsdem diſtantijs
                <expan abbr="eidẽ">eidem</expan>
                <expan abbr="põ">pom</expan>
                <lb/>
              deri pondus quandoquè maius, quandoquè minus ę〈que〉pon­
                <lb/>
              derare non poſſit; vt in hoc caſu accidere poteſt. </s>
              <s id="N11A4F">Quocirca
                <lb/>
              nec propriè dici poſſunt pondera, ſiue in libra AB, ſiue ex
                <lb/>
              diſtantijs CA CB conſtituta eſſe. </s>
              <s id="N11A55">Vndè ne〈que〉 Archimedis
                <lb/>
              propoſitiones in hoc caſu ſunt intelligendę quandoquidem
                <lb/>
              in his propriè quærit ponderum, magnitudinumquè æ〈que〉­
                <lb/>
              ponderationes. </s>
              <s id="N11A5D">ne〈que〉 enim in hac quarta demonſtratione in
                <lb/>
              hoc caſu potuiſſet Archimedes abſurdum oſtendere, ſi C
                <expan abbr="nõ">non</expan>
                <lb/>
              eſt grauitatis centrum magnitudinis ex AB compoſitæ, ſit
                <lb/>
              E. facta igitur ex E ſuſpenſione, magnitudines æquales AB
                <lb/>
              ex in æqualibus diſtantijs EA EB ę〈que〉ponderabunt. </s>
              <s id="N11A6B">quod
                <lb/>
              fieri non poteſt. </s>
              <s id="N11A6F">non enim hoc eſt abſurdum; cùm pondera
                <lb/>
              ex E ſuſpenſa
                <expan abbr="maneãt">maneant</expan>
              idcirco quando linea AB eſt
                <expan abbr="horizõ">horizom</expan>
                <lb/>
              ti erecta; propriè ad rem noſtram minimè pertinet. </s>
              <s id="N11A7D">Ex dictis
                <lb/>
              igitur ſemper valet conſe〈que〉ntia, hoc punctum horum pon
                <lb/>
              derum centrum eſt grauitatis, ergo ſi ex hoc ſuſpendantur,
                <expan abbr="põ">pom</expan>
                <lb/>
              dera ę〈que〉ponderant. </s>
              <s id="N11A89">non autem è conuerſo. </s>
              <s id="N11A8B">niſi quando ar­
                <lb/>
              gumentatio ſumitur ſemper ex recta linea, quæ centra graui
                <lb/>
              tatis magnitudinum coniungit, & quando hęc linea non eſt
                <lb/>
                <arrow.to.target n="fig22"/>
                <lb/>
              horizonti erecta. </s>
              <s id="N11A98">hac enim
                <lb/>
              ratione quocun〈que〉 modo
                <lb/>
              recta linea ſe habeat, ſem­
                <lb/>
              per ſequitur idem. </s>
              <s id="N11AA0">Vt ſi li­
                <lb/>
              nea AB fuerit, ſiue
                <expan abbr="nõ">non</expan>
              fue­
                <lb/>
              rit horizonti æquidiſtans,
                <lb/>
              ipſius medium C centrum
                <lb/>
              erit grauitatis magnitudi­
                <lb/>
              nis ex magnitudinibus AB æqualibus compoſitę. </s>
              <s id="N11AB0">vnde ſequi</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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