Huygens, Christiaan, Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica

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        <div xml:id="echoid-div159" type="section" level="1" n="73">
          <p>
            <s xml:id="echoid-s3039" xml:space="preserve">
              <pb o="424" file="0142" n="151" rhead="VERA CIRCULI"/>
            dicta quantitas eodem etiam modo componitur ex ul-
              <lb/>
            timis ejus terminis convergentibus, qui æquales ſunt:
              <lb/>
            </s>
            <s xml:id="echoid-s3040" xml:space="preserve">ſit ultimus ille terminus
              <emph style="super">x</emph>
            qui multiplicatus in {mae-mbe/ad-bd} & </s>
            <s xml:id="echoid-s3041" xml:space="preserve">
              <lb/>
            in
              <emph style="super">m</emph>
            efficit xm & </s>
            <s xml:id="echoid-s3042" xml:space="preserve">{xmae - xmbe/ad - bd}, quorum factorum ſumma nempe
              <lb/>
            {xmae - xmbe + xmad - xmbd/ad - bd} æquatur {maae - mbae + mbad - mbbd/ad - bd} & </s>
            <s xml:id="echoid-s3043" xml:space="preserve">æquatio-
              <lb/>
            ne reducta invenitur x ſeu ſeriei terminatio {aae - bae + bad - bbd/ae - be + ad - bd},
              <lb/>
            quam invenire oportuit.</s>
            <s xml:id="echoid-s3044" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3045" xml:space="preserve">Ne minus exercitatis obſcurum videatur hoc problema,
              <lb/>
            illud in numeris illuſtrabimus: </s>
            <s xml:id="echoid-s3046" xml:space="preserve">ſit
              <emph style="super">c 7, d 2, e 3, a 28, b 42,</emph>
            erunt ſe-
              <lb/>
            cundi termini convergentes 32, 36, tertii 33 {1/7}, 34 {2/7}, & </s>
            <s xml:id="echoid-s3047" xml:space="preserve">ejus ter-
              <lb/>
            minatio 33 {3/5}.</s>
            <s xml:id="echoid-s3048" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3049" xml:space="preserve">Neminem moveat, quod (etiamſi
              <emph style="super">a</emph>
            ſit minor quam
              <emph style="super">b</emph>
            )
              <lb/>
            {ca + bd - ad/c} poſſit eſſe major quam {bc - be + ae/c}, analyticè enim major
              <lb/>
            à minore poteſt ſubſtrahi, cnjus tamen exemplum non grava-
              <lb/>
            bimus exhibere, ſit
              <emph style="super">c 7, d 5, e 4, a 28, b 42;</emph>
            erunt ſecundi termini
              <lb/>
            convergentes 38, 34, & </s>
            <s xml:id="echoid-s3050" xml:space="preserve">tertii 35 {1/7}, 36 {2/7}, ejuſque terminatio
              <lb/>
            35 {7/9}.</s>
            <s xml:id="echoid-s3051" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3052" xml:space="preserve">Animadvertendum eſt hujus problematis ſolutionem eo-
              <lb/>
            dem modo ſe habere, etiamſi loco
              <emph style="super">a</emph>
            ponatur cyphra ſeu me-
              <lb/>
            rum nihil, Ex. </s>
            <s xml:id="echoid-s3053" xml:space="preserve">Gr; </s>
            <s xml:id="echoid-s3054" xml:space="preserve">ſit
              <emph style="super">c 8, d 3, e 4, a 0, b 24;</emph>
            erunt ſecundi ter-
              <lb/>
            mini convergentes 9, 12, & </s>
            <s xml:id="echoid-s3055" xml:space="preserve">tertii 10 {1/8}, 10 {1/2}, & </s>
            <s xml:id="echoid-s3056" xml:space="preserve">ſeriei termina-
              <lb/>
            tio 10 {2/7},</s>
          </p>
          <p>
            <s xml:id="echoid-s3057" xml:space="preserve">Harum etiam ſerierum terminationes poſſunt inveniri ex
              <lb/>
            Gregorii à S. </s>
            <s xml:id="echoid-s3058" xml:space="preserve">Vincentio lib. </s>
            <s xml:id="echoid-s3059" xml:space="preserve">de progreſſ. </s>
            <s xml:id="echoid-s3060" xml:space="preserve">geometrica, etiamſi
              <lb/>
            methodo longe ab hac diverſa.</s>
            <s xml:id="echoid-s3061" xml:space="preserve"/>
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