Ceva, Giovanni, Geometria motus, 1692

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s id="s.000907">
                <pb pagenum="93" xlink:href="022/01/099.jpg"/>
              ſit vtrationes AE ad EB, AF ad FC, AG ad GD, AI ad
                <lb/>
              IH, AK ad KL ſint æquales. </s>
              <s id="s.000908">Sunt pariter æquales reſi­
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              ſtentiæ elateriorum in B, C, D, H, L (poſuimus enim ela­
                <lb/>
              teria ita opportunè aucta vt æquè facile ſingula aperian­
                <lb/>
              tur) ergo (ex primis principijs mechanicorum) dum attra­
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              huntur fune extrema capita A, N, eodem tempore, eadem­
                <lb/>
              que facili ate vincetur æquilibrium omnium elateriorum,
                <lb/>
              quorum reſiſtentia in ſingulis conſideratur in ratione pon­
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              deris, quemadmodum lineæ AE, EB; AF, FC; AG, GD
                <lb/>
              &c. conſiderantur vt vectes, quorum hippomoclia ſeu
                <expan abbr="cẽ-tra">cen­
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                tra</expan>
              ſunt in E, F, G, I, K, potentia autem conſideratur in A
                <lb/>
              communis omnibus. </s>
            </p>
            <p type="main">
              <s id="s.000909">Secundò, cùm AE ad EB (idem die de cæteris) habeant
                <lb/>
              magnam proportionem, facilè aperientur nodi, & curuabi­
                <lb/>
              tur arcus; quantumuis augeatur numerus nodorum. </s>
            </p>
            <p type="main">
              <s id="s.000910">Tertiò Cum ſint plures nodi, atque omnes aperiantur,
                <lb/>
              neceſſe eſt vt brachia arcus valdè incuruentur;
                <expan abbr="quamobrẽ">quamobrem</expan>
                <lb/>
              ſi idem arcus ſibi relinquatur, prædicti nodi omnes, vi ela­
                <lb/>
              teriorum, ictu oculi claudentur; eodemque puncto tempo­
                <lb/>
              ris corda ex O percurret totum ſpatium vſque ad M: Quòd
                <lb/>
              cùm fieri nequeat niſi ſumma velocitate, propter magni­
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              tudinem prædicti ſpatij, & velocitati reſpondent vis, atque
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              impetus, neceſſe eſt vt hinc ſequatur ictus valde notabilis,
                <lb/>
              vt facilè eſt vnicuique conijcere. </s>
            </p>
            <p type="main">
              <s id="s.000911">Super ſunt nunc difficultates nonnullæ ſoluendæ. </s>
              <s id="s.000912">Prima
                <lb/>
              eſt, quòd licèt vis ſufficiens in A ad vincendum
                <expan abbr="æquilibriũ">æquilibrium</expan>
                <lb/>
              elaterij B, illa eadem quoque ſufficiat ad vincendum æqui­
                <lb/>
              librium cæterorum, propter æquales proportiones
                <expan abbr="vectiũ">vectium</expan>
              ;
                <lb/>
              his tamen non obſtantibus, ſi conſideretur brachium iam
                <lb/>
              incuruatum, vt apparet in KLA punctis notato, proportio­
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              nes illæ cernuntur notabiliter variatæ. </s>
              <s id="s.000913">Neque enim pro
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              longitudinibus vectium ſumi poſſunt longitudines priores,
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              ſed loco ipſarum accipiendæ ſunt applicatæ arcus, videli­
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              cet af, ag, ai, ak quarum ak, eidemque propinquiores,
                <expan abbr="quã-">quan-</expan>
              </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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