Ceva, Giovanni, Geometria motus, 1692

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    <archimedes>
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        <body>
          <chap>
            <pb pagenum="50" xlink:href="022/01/056.jpg"/>
            <p type="margin">
              <s id="s.000517">
                <margin.target id="marg116"/>
                <emph type="italics"/>
              Pr
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              2.
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              primą
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              huius.
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              </s>
            </p>
            <p type="main">
              <s id="s.000518">
                <emph type="center"/>
                <emph type="italics"/>
              Corollarium. III.
                <emph.end type="italics"/>
                <emph.end type="center"/>
              </s>
            </p>
            <p type="main">
              <s id="s.000519">
                <emph type="italics"/>
              Illud etiam conſtat, eſſe in vtroque caſu vt quadrilineum
                <lb/>
              HIRP ad ipſum PRSM, ita AF ad FD.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="s.000520">
                <emph type="center"/>
              PROP. XIV. THEOR. X.
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              </s>
            </p>
            <p type="main">
              <s id="s.000521">PRopoſitis Spirali Archimedea primæ circulationis
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              ABD, et AGF
                <expan abbr="cõmuni">communi</expan>
              parabola, ſit FG baſis huius
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              æqualis radio DA, et GA ſit dimidium circumferentię cir­
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              culi AEG; erit parabola AGF axem habens GA æqualis
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              propoſitæ ſpirali. </s>
            </p>
            <p type="margin">
              <s id="s.000522">
                <margin.target id="marg117"/>
                <emph type="italics"/>
              Tab.
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              5.
                <emph type="italics"/>
              fig.
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              3.</s>
            </p>
            <p type="main">
              <s id="s.000523">Sit PNK communis hyperbola, cuius coniugati ſemia­
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                <arrow.to.target n="marg118"/>
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              xes ſint IK, IH, & aſſymptotos IO. </s>
              <s id="s.000524">Eſto etiam axis hy­
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              perbolæ huius, dupla ſcilicet IK, ad HO illi ęquidiſtantem
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              vt FG ad AG. </s>
              <s id="s.000525">Iam conſtat quadrilineum IHPK fore ima­
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              ginem velocitatum, iuxta quam curreretur parabola AGF
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              tempore IH: ſi modo oſtendimus hoc ipſum
                <expan abbr="quadrilineũ">quadrilineum</expan>
                <lb/>
              eſſe pariter homogeneam imaginem alterius compoſiti
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              motus, quo videlicet deſcribitur ſpiralis propoſita ABD,
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                <arrow.to.target n="marg119"/>
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              palam erit, ipſam parabolam eidem illi ſpirali æqualem fu­
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              turam. </s>
              <s id="s.000526">Ducatur recta KL, quæ æquidiſtet IH; item ex
                <lb/>
              quouis puncto Q
                <expan abbr="tẽporis">temporis</expan>
              IH alia deducatur recta QRMN
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              parallela IK: erit parallelogrammum rectangulum HIKL
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              imago velocitatum, iuxta quam curritur FG, et HIO trian­
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              gulum imago, qua curritur AG motu grauium deſcenden­
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              tium: Verùm quia eodem tempore IH, ſi mobile currat
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              æquabili motu DA æqualem FG, eſt eius imago idem re­
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              ctangulum IHKL, curriturque illo eodem tempore IH (ſpi­
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              rali exigente) omnis circuli circunferentia AGEA æqua­
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              bili etiam motu ab extremitate A radij AD circumducti in
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              deſcriptione ſpiralis; ob idque factum eſt, vt IK ad HO eſ­
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              ſet vt DA ad circunferentiam ipſam AGEA; nam hoc mo-</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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